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

<b>let </b><font color="Maroon">G</font> be  <a href="glib_000.html#V2">finite</a> <a href="glib_003.html#V7">real-weighted</a> <a href="glib_003.html#V9">real-elabeled</a> <a href="glib_005.html#V1" target="_self">complete-elabeled</a> <a href="glib_003.html#NM4">WEGraph</a>;<br/><b>let </b><font color="Maroon">source</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">sink</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">V</font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:74"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">G</font> <a href="glib_005.html#R1" target="_self">has_valid_flow_from</a> <font color="Maroon">source</font>,<font color="Maroon">sink</font> &amp; <font color="Maroon">source</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> &amp; not <font color="Maroon">sink</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> )
 ;<br/>

<b>set </b><font color="Maroon">EL</font> =  <a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font>;<br/>
<b>set </b><font color="Maroon">VG</font> =  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>for <font color="Olive">V</font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>  st  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Olive">V</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Maroon">source</font> <a href="hidden.html#R2">in</a> <font color="Olive">V</font> &amp; not <font color="Maroon">sink</font> <a href="hidden.html#R2">in</a> <font color="Olive">V</font> holds <br/><font color="Maroon">G</font> <a href="glib_005.html#K2" target="_self">.flow</a> <font color="Maroon">source</font>,<font color="Maroon">sink</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Olive">V</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Olive">V</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Olive">V</font></span>)</span>,<font color="Olive">V</font></span>)</span></span>)</span></span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">V</font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>;<br/><b>assume </b><a NAME="E1:74_1"/><i><font color="Green">E51</font></i>: 
(  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">source</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> &amp; not <font color="Maroon">sink</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> )
 ;<br/><b>then consider </b><font color="Maroon">v</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:74_1"/><i><font color="Green">E82</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="card_2.html#T60">CARD_2:60</a></i>;<br/><a NAME="E4:74_1"/>
<font color="Maroon">sink</font> is   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>
 <b>by </b><i>, </i>;<br/><a NAME="E5:74_1"/><b>then </b>
<font color="Maroon">sink</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:74_1"/><b>then </b><i><font color="Green">E89</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">sink</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><div><i><font color="Green">E92</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:74_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:74_1_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E3:74_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:74_1_1"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font>
 ;<br/><a NAME="E3:74_1_1"/><b>then </b>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:74_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:74"><i><font color="Green">E37</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div><a NAME="E8:74_1"/><b>then </b><i><font color="Green">E94</font></i>: 
<font color="Maroon">V</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><b>set </b><font color="Maroon">ESS</font> = <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>;<br/><b>reconsider </b><font color="Maroon">EIN</font> = <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font></span>)</span> ;<br/><b>reconsider </b><font color="Maroon">EOUT</font> = <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font></span>)</span> ;<br/><b>set </b><font color="Maroon">EESS</font> = <span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:74_1_2_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span>
 ;<br/><a NAME="E2:74_1_2_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i>, , <a class="txt" href="glib_005.html#E1:74"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_1_2_1"/><b>then </b><i><font color="Green">E95</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_1_2_1"/><b>then </b><i><font color="Green">E96</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D28">GLIB_000:def 28</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:74_1_2_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:74_1_2_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_1_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E4:74_1_2_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:74_1_2_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EIN</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:74_1_2"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EIN</font>
 ;<br/><a NAME="E3:74_1_2"/><b>then </b><i><font color="Green">E110</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> &amp; not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:74_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span>
 ;<br/><a NAME="E5:74_1_2"/><b>then </b><i><font color="Green">E111</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i>, <a class="ref" href="glib_000.html#D28">GLIB_000:def 28</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:74_1_2_2"/>
not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font>
 ;<br/><a NAME="E2:74_1_2_2"/><b>then </b><i><font color="Green">E112</font></i>: 
not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i/>;<br/><a NAME="E3:74_1_2_2"/>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/><a NAME="E4:74_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_005.html#D1" target="_self">Def1</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E5:74_1_2_2"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E6:74_1_2_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div><b>end;</b></div><a NAME="E7:74_1_2"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E8:74_1_2"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div><b>end;</b></div><a NAME="E12:74_1"/><b>then </b><i><font color="Green">E128</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">EIN</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_1_3"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:74_1_3"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_1_3"/><b>then </b>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E4:74_1_3"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D28">GLIB_000:def 28</a></i>;<br/></div><b>end;</b></div><a NAME="E14:74_1"/><b>then </b><i><font color="Green">E129</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/><i><font color="Green">E130</font></i>: <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">EIN</font> = 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/><a NAME="E16:74_1"/><i><font color="Green">E131</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EIN</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">EIN</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EOUT</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">EOUT</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E17:74_1"/><b>then </b><i><font color="Green">E132</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EIN</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">EIN</font>
 <b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_1_5"/><i><font color="Green">E133</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:74_1_5"/><b>then </b><i><font color="Green">E134</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_1_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_1_5_1_1"/>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> or  not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_1_5_1_1_1"><b>suppose </b></a><a NAME="E1:74_1_5_1_1_1"/><i><font color="Green">E135</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_1_5_1_1_1"/><b>then </b>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EIN</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EIN</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_005.html#D1" target="_self">Def1</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="glib_005.html#D1" target="_self">Def1</a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_1_5_1_1_2"><b>suppose </b></a><a NAME="E1:74_1_5_1_1_2"/>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_1_5_1_1_2"/><b>then </b><i><font color="Green">E137</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EIN</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EIN</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EIN</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_005.html#D1" target="_self">Def1</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="glib_005.html#D1" target="_self">Def1</a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:74_1_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EIN</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>;<br/></div><b>end;</b></div><a NAME="E19:74_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EIN</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="glib_005.html#D1" target="_self">Def1</a>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E20:74_1"/><b>then </b><i><font color="Green">E138</font></i>: 
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EIN</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_004.html#T3">GLIB_004:3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:74_1_6_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span>,<font color="Maroon">V</font>
 ;<br/><a NAME="E2:74_1_6_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i>, , <a class="txt" href="glib_005.html#E1:74"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_1_6_1"/><b>then </b><i><font color="Green">E139</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_1_6_1"/><b>then </b><i><font color="Green">E140</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D29">GLIB_000:def 29</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_6_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:74_1_6_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:74_1_6_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_1_6_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E4:74_1_6_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:74_1_6_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EOUT</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:74_1_6"/><i><font color="Green">E141</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EOUT</font>
 ;<br/><a NAME="E3:74_1_6"/><b>then </b><i><font color="Green">E142</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> &amp; not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:74_1_6"/>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span>
 ;<br/><a NAME="E5:74_1_6"/><b>then </b><i><font color="Green">E143</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D29">GLIB_000:def 29</a>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_6_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:74_1_6_2"/><i><font color="Green">E144</font></i>: 
not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font>
 ;<br/><a NAME="E2:74_1_6_2"/>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/><a NAME="E3:74_1_6_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_005.html#D3" target="_self">Def3</a>, <a class="txt" href="glib_005.html#E1:74"><i><font color="Green">E37</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:74_1_6_2"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D2" target="_self">Def2</a>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E5:74_1_6_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div><b>end;</b></div><a NAME="E7:74_1_6"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font>,<font color="Maroon">V</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D2" target="_self">Def2</a>, , , <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E8:74_1_6"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span>,<font color="Maroon">V</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div><b>end;</b></div><a NAME="E22:74_1"/><b>then </b><i><font color="Green">E145</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span>,<font color="Maroon">V</font> <a href="hidden.html#R1">=</a> <font color="Maroon">EOUT</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_7"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_1_7"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:74_1_7"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_1_7"/><b>then </b>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E4:74_1_7"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D29">GLIB_000:def 29</a></i>;<br/></div><b>end;</b></div><a NAME="E24:74_1"/><b>then </b><i><font color="Green">E146</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">EOUT</font> = 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/><a NAME="E26:74_1"/><b>then </b><i><font color="Green">E147</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EOUT</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_005.html#D1" target="_self">Def1</a>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_9"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_1_9"/><i><font color="Green">E148</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:74_1_9"/><b>then </b><i><font color="Green">E149</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_9_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_1_9_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_1_9_1_1"/>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> or  not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_1_9_1_1_1"><b>suppose </b></a><a NAME="E1:74_1_9_1_1_1"/><i><font color="Green">E150</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_1_9_1_1_1"/><b>then </b>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EOUT</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EOUT</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_005.html#D1" target="_self">Def1</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_005.html#D5" target="_self">Def5</a>, <a class="ref" href="glib_005.html#D1" target="_self">Def1</a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_1_9_1_1_2"><b>suppose </b></a><a NAME="E1:74_1_9_1_1_2"/>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_1_9_1_1_2"/><b>then </b><i><font color="Green">E151</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EOUT</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D4" target="_self">Def4</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EOUT</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EOUT</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_005.html#D1" target="_self">Def1</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_005.html#D5" target="_self">Def5</a>, <a class="ref" href="glib_005.html#D1" target="_self">Def1</a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:74_1_9"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EOUT</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D3" target="_self">Def3</a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>;<br/></div><b>end;</b></div><a NAME="E28:74_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EOUT</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D1" target="_self">Def1</a>, <a class="ref" href="glib_005.html#D2" target="_self">Def2</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E29:74_1"/><b>then </b>
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EOUT</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_004.html#T3">GLIB_004:3</a></i>;<br/><b>then </b><font color="Maroon">G</font> <a href="glib_005.html#K2" target="_self">.flow</a> <font color="Maroon">source</font>,<font color="Maroon">sink</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EIN</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span>,<span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EOUT</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EIN</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EOUT</font></span>)</span></span>)</span>

;<br/><b>hence </b><a NAME="E31:74_1"/>
<font color="Maroon">G</font> <a href="glib_005.html#K2" target="_self">.flow</a> <font color="Maroon">source</font>,<font color="Maroon">sink</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span>,<font color="Maroon">V</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<a NAME="E3:74"/><b>then </b><i><font color="Green">E152</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[1]
 
;<br/>
<div><i><font color="Green">E153</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:74_2"/><i><font color="Green">E154</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">n</font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">V2</font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>;<br/><b>assume </b><a NAME="E1:74_2_1"/><i><font color="Green">E155</font></i>: 
(  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">source</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font> &amp; not <font color="Maroon">sink</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font> )
 ;<br/><b>set </b><font color="Maroon">x</font> =  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span>;<br/><a NAME="E2:74_2_1"/><i><font color="Green">E156</font></i>: 
<font color="Maroon">V2</font> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">V2</font>
 ;<br/><a NAME="E3:74_2_1"/>
<font color="Maroon">sink</font> is   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>
 <b>by </b><i>, </i>;<br/><a NAME="E4:74_2_1"/><b>then </b>
<font color="Maroon">sink</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E5:74_2_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/><b>then </b> <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="card_2.html#T63">CARD_2:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1
<b>by </b><i><a class="ref" href="card_1.html#T79">CARD_1:79</a></i>
<br/>.= 
<font color="Maroon">n</font>

;<br/><a NAME="E7:74_2_1"/><b>then </b><i><font color="Green">E157</font></i>: 
(  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font> &amp; not  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="card_1.html#T78">CARD_1:78</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E8:74_2_1"/><b>then </b><i><font color="Green">E158</font></i>: 
(  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> &amp; not  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>set </b><font color="Maroon">V1</font> = <font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>;<br/><b>set </b><font color="Maroon">EV1V1a</font> = <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">EV1V1b</font> = <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>;<br/><b>set </b><font color="Maroon">EV2X</font> = <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>;<br/><b>set </b><font color="Maroon">EXV2</font> = <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>;<br/><b>set </b><font color="Maroon">EXV1c</font> = <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">EV1Xd</font> = <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>;<br/><a NAME="E9:74_2_1"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/><b>then reconsider </b><font color="Maroon">V1</font> = <font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <b>by </b><i><a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/><a NAME="E11:74_2_1"/><i><font color="Green">E159</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T41">XBOOLE_1:41</a></i>;<br/><a NAME="E12:74_2_1"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/><b>then </b><i><font color="Green">E160</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="card_2.html#T63">CARD_2:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1
<b>by </b><i>, <a class="ref" href="card_1.html#T79">CARD_1:79</a></i>
<br/>.= 
<font color="Maroon">n</font>

;<br/><a NAME="E14:74_2_1"/><i><font color="Green">E161</font></i>: 
<font color="Maroon">source</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E15:74_2_1"/><i><font color="Green">E162</font></i>: 
 <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">sink</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E16:74_2_1"/><b>then </b>
not <font color="Maroon">sink</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E17:74_2_1"/><b>then </b>
not <font color="Maroon">sink</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E18:74_2_1"/><b>then </b><i><font color="Green">E163</font></i>: 
<font color="Maroon">G</font> <a href="glib_005.html#K2" target="_self">.flow</a> <font color="Maroon">source</font>,<font color="Maroon">sink</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="glib_005.html#D1" target="_self">Def1</a>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:74_2_1_3_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span>
 ;<br/><a NAME="E2:74_2_1_3_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V2</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_2_1_3_1"/><b>then </b><i><font color="Green">E164</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_2_1_3_1"/><b>then </b><i><font color="Green">E165</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div><i><font color="Green">E166</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_3_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:74_2_1_3_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:74_2_1_3_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_2_1_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E4:74_2_1_3_1_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_3_1_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_3_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_2_1_3_1_2_1"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> or  not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_3_1_2_1_1"><b>suppose </b></a><a NAME="E1:74_2_1_3_1_2_1_1"/>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_3_1_2_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E3:74_2_1_3_1_2_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E4:74_2_1_3_1_2_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E5:74_2_1_3_1_2_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D3" target="_self">Def3</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_3_1_2_1_2"><b>suppose </b></a><a NAME="E1:74_2_1_3_1_2_1_2"/>
not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_3_1_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E3:74_2_1_3_1_2_1_2"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V1</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_005.html#D2" target="_self">Def2</a>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_2_1_3_1_2_1_2"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E5:74_2_1_3_1_2_1_2"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E6:74_2_1_3_1_2_1_2"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D3" target="_self">Def3</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E7:74_2_1_3_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 ;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:74_2_1_3"/><i><font color="Green">E167</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E3:74_2_1_3"/><b>then </b>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> &amp; not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:74_2_1_3"/><b>then </b><i><font color="Green">E168</font></i>: 
not <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E5:74_2_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E6:74_2_1_3"/><b>then </b><i><font color="Green">E169</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i/>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_3_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_3_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_2_1_3_2_1"/>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> or <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 </span><b>by </b><i><a class="ref" href="glib_005.html#D3" target="_self">Def3</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_3_2_1_1"><b>suppose </b></a><a NAME="E1:74_2_1_3_2_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_3_2_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V1</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_2_1_3_2_1_1"/><b>then </b><i><font color="Green">E170</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_2_1_3_2_1_1"/><b>then </b>
not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_005.html#D2" target="_self">Def2</a>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E5:74_2_1_3_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_005.html#D4" target="_self">Def4</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:74_2_1_3_2_1_1"/><b>then </b><i><font color="Green">E171</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T40">XBOOLE_1:40</a></i>;<br/><a NAME="E7:74_2_1_3_2_1_1"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> &amp; not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font> )
 <b>by </b><i><a class="ref" href="glib_005.html#D4" target="_self">Def4</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E8:74_2_1_3_2_1_1"/><b>then </b>
not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E9:74_2_1_3_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D4" target="_self">Def4</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E10:74_2_1_3_2_1_1"/>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V2</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D4" target="_self">Def4</a>, <a class="ref" href="glib_005.html#D5" target="_self">Def5</a>, <a class="txt" href="glib_005.html#E1:74"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_3_2_1_2"><b>suppose </b></a><a NAME="E1:74_2_1_3_2_1_2"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_3_2_1_2"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_2_1_3_2_1_2"/><b>then </b><i><font color="Green">E172</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_2_1_3_2_1_2"/><i><font color="Green">E173</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D4" target="_self">Def4</a>, <a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/><a NAME="E5:74_2_1_3_2_1_2"/>
not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font>
 <b>by </b><i>, <a class="ref" href="glib_005.html#D4" target="_self">Def4</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E6:74_2_1_3_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D5" target="_self">Def5</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E7:74_2_1_3_2_1_2"/>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V2</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D4" target="_self">Def4</a>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E8:74_2_1_3"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div><b>end;</b></div><a NAME="E20:74_2_1"/><b>then </b><i><font color="Green">E174</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><b>reconsider </b><font color="Maroon">EA</font> = <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font></span>)</span> ;<br/><b>reconsider </b><font color="Maroon">E1</font> = <font color="Maroon">EA</font> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font></span>)</span> ;<br/><b>reconsider </b><font color="Maroon">EB</font> = <font color="Maroon">EA</font> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font></span>)</span> ;<br/><b>reconsider </b><font color="Maroon">EC</font> = <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font></span>)</span> ;<br/><b>reconsider </b><font color="Maroon">E2</font> = <font color="Maroon">EC</font> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font></span>)</span> ;<br/><b>reconsider </b><font color="Maroon">ED</font> = <font color="Maroon">EC</font> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font></span>)</span> ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:74_2_1_4"/>
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:74_2_1_4"/><b>then </b><i><font color="Green">E175</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><b>set </b><font color="Maroon">e</font> =  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>;<br/><a NAME="E3:74_2_1_4"/>
(  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> &amp;  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_005.html#D2" target="_self">Def2</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:74_2_1_4"/><b>then </b>
(  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V1</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<font color="Maroon">G</font> &amp;  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E5:74_2_1_4"/><b>then </b>
( <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E6:74_2_1_4"/><b>then </b>
( not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E7:74_2_1_4"/>
contradiction
 ;<br/></div><b>end;</b></div><a NAME="E28:74_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T83">XBOOLE_1:83</a></i>;<br/><a NAME="E29:74_2_1"/><b>then </b><i><font color="Green">E176</font></i>: 
<font color="Maroon">EB</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T40">XBOOLE_1:40</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:74_2_1_5"/>
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>
 ;<br/><a NAME="E2:74_2_1_5"/><b>then </b><i><font color="Green">E177</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><b>set </b><font color="Maroon">e</font> =  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span>;<br/><a NAME="E3:74_2_1_5"/>
(  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> &amp;  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font> )
 <b>by </b><i><a class="ref" href="glib_005.html#D3" target="_self">Def3</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:74_2_1_5"/><b>then </b>
(  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<font color="Maroon">V1</font>,<font color="Maroon">G</font> &amp;  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>,<font color="Maroon">G</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E5:74_2_1_5"/><b>then </b>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E6:74_2_1_5"/><b>then </b>
( not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E7:74_2_1_5"/>
contradiction
 ;<br/></div><b>end;</b></div><a NAME="E31:74_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T83">XBOOLE_1:83</a></i>;<br/><a NAME="E32:74_2_1"/><b>then </b><i><font color="Green">E178</font></i>: 
<font color="Maroon">ED</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T40">XBOOLE_1:40</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_2_1_6"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:74_2_1_6"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_2_1_6"/><b>then </b><i><font color="Green">E179</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_2_1_6"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E5:74_2_1_6"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V1</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D4" target="_self">Def4</a>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E6:74_2_1_6"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div><b>end;</b></div><a NAME="E34:74_2_1"/><b>then </b>
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/><a NAME="E35:74_2_1"/><b>then </b><i><font color="Green">E180</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T10">XBOOLE_1:10</a></i>;<br/><a NAME="E36:74_2_1"/><i><font color="Green">E181</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EA</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">EA</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EB</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">EB</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">EA</font> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><b>then </b><i><font color="Green">E182</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E1</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">EA</font> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
<br/>.= 
<font color="Maroon">EA</font>
<b>by </b><i><a class="ref" href="glib_005.html#D4" target="_self">Def4</a>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_2_1_8"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EA</font></span>)</span>
 ;<br/><a NAME="E2:74_2_1_8"/><b>then </b><i><font color="Green">E183</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EA</font>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_8_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_2_1_8_1_1"/>
(  not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> or <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_8_1_1_1"><b>suppose </b></a><a NAME="E1:74_2_1_8_1_1_1"/>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_8_1_1_1"/><b>then </b><i><font color="Green">E184</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">E1</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E1</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E1</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_005.html#D5" target="_self">Def5</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_8_1_1_2"><b>suppose </b></a><a NAME="E1:74_2_1_8_1_1_2"/><i><font color="Green">E185</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_8_1_1_2"/><b>then </b>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">E1</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E1</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_005.html#D5" target="_self">Def5</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:74_2_1_8"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EA</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E1</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/></div><b>end;</b></div><a NAME="E39:74_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EA</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E1</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D5" target="_self">Def5</a>, <a class="ref" href="glib_005.html#D6" target="_self">Def6</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E40:74_2_1"/><b>then </b>
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EA</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_004.html#T3">GLIB_004:3</a></i>;<br/><a NAME="E41:74_2_1"/><b>then </b><i><font color="Green">E186</font></i>: 
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EA</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><i><font color="Green">E187</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EB</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">EB</font>
<b>by </b><i><a class="ref" href="glib_005.html#D5" target="_self">Def5</a>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
<br/>.= 
<font color="Maroon">EA</font>
<b>by </b><i><a class="ref" href="xboole_1.html#T6">XBOOLE_1:6</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_10"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_2_1_10"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EA</font></span>)</span>
 ;<br/><a NAME="E2:74_2_1_10"/><b>then </b><i><font color="Green">E188</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EA</font>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_10_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_10_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_2_1_10_1_1"/>
(  not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_10_1_1_1"><b>suppose </b></a><a NAME="E1:74_2_1_10_1_1_1"/>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_10_1_1_1"/><b>then </b><i><font color="Green">E189</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EB</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EB</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EB</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_005.html#D5" target="_self">Def5</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_10_1_1_2"><b>suppose </b></a><a NAME="E1:74_2_1_10_1_1_2"/><i><font color="Green">E190</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_10_1_1_2"/><b>then </b>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EB</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EB</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_005.html#D5" target="_self">Def5</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:74_2_1_10"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EA</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EB</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/></div><b>end;</b></div><a NAME="E44:74_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EA</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EB</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D5" target="_self">Def5</a>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E45:74_2_1"/><b>then </b><i><font color="Green">E191</font></i>: 
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EA</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D2" target="_self">Def2</a>, <a class="ref" href="glib_004.html#T3">GLIB_004:3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_11"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_2_1_11"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:74_2_1_11"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_2_1_11"/><b>then </b><i><font color="Green">E192</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_2_1_11"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E5:74_2_1_11"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<font color="Maroon">V1</font>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E6:74_2_1_11"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div><b>end;</b></div><a NAME="E47:74_2_1"/><b>then </b>
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/><a NAME="E48:74_2_1"/><b>then </b><i><font color="Green">E193</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T10">XBOOLE_1:10</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_12"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:74_2_1_12_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span>,<font color="Maroon">V2</font>
 ;<br/><a NAME="E2:74_2_1_12_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font>,<font color="Maroon">V2</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_2_1_12_1"/><b>then </b><i><font color="Green">E194</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_2_1_12_1"/><b>then </b><i><font color="Green">E195</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div><i><font color="Green">E196</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_12_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:74_2_1_12_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:74_2_1_12_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_2_1_12_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E4:74_2_1_12_1_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_12_1_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_12_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_2_1_12_1_2_1"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> or  not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_12_1_2_1_1"><b>suppose </b></a><a NAME="E1:74_2_1_12_1_2_1_1"/>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_12_1_2_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E3:74_2_1_12_1_2_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E4:74_2_1_12_1_2_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E5:74_2_1_12_1_2_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_12_1_2_1_2"><b>suppose </b></a><a NAME="E1:74_2_1_12_1_2_1_2"/>
not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_12_1_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E3:74_2_1_12_1_2_1_2"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<font color="Maroon">V1</font>,<font color="Maroon">G</font>
 <b>by </b><i>, , <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_2_1_12_1_2_1_2"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E5:74_2_1_12_1_2_1_2"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E6:74_2_1_12_1_2_1_2"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E7:74_2_1_12_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 ;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:74_2_1_12"/><i><font color="Green">E197</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 ;<br/><a NAME="E3:74_2_1_12"/><b>then </b>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span> &amp; not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:74_2_1_12"/><b>then </b><i><font color="Green">E198</font></i>: 
not <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E5:74_2_1_12"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span>
 ;<br/><a NAME="E6:74_2_1_12"/><b>then </b><i><font color="Green">E199</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span>
 <b>by </b><i/>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_12_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_12_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_2_1_12_2_1"/>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> or <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font> )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_12_2_1_1"><b>suppose </b></a><a NAME="E1:74_2_1_12_2_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_12_2_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<font color="Maroon">V1</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_2_1_12_2_1_1"/><b>then </b><i><font color="Green">E200</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_2_1_12_2_1_1"/><b>then </b>
not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E5:74_2_1_12_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:74_2_1_12_2_1_1"/><b>then </b><i><font color="Green">E201</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T40">XBOOLE_1:40</a></i>;<br/><a NAME="E7:74_2_1_12_2_1_1"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> &amp; not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font> )
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E8:74_2_1_12_2_1_1"/><b>then </b>
not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E9:74_2_1_12_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E10:74_2_1_12_2_1_1"/>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font>,<font color="Maroon">V2</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:74"><i><font color="Green">E37</font></i></a>, , , <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_12_2_1_2"><b>suppose </b></a><a NAME="E1:74_2_1_12_2_1_2"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>
 ;<br/><div class="add"><a NAME="E2:74_2_1_12_2_1_2"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_2_1_12_2_1_2"/><b>then </b><i><font color="Green">E202</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_2_1_12_2_1_2"/><i><font color="Green">E203</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/><a NAME="E5:74_2_1_12_2_1_2"/>
not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font>
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E6:74_2_1_12_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E7:74_2_1_12_2_1_2"/>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font>,<font color="Maroon">V2</font>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E8:74_2_1_12"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span>,<font color="Maroon">V2</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div><b>end;</b></div><a NAME="E50:74_2_1"/><b>then </b><i><font color="Green">E204</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span>,<font color="Maroon">V2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E2</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><a NAME="E51:74_2_1"/><i><font color="Green">E205</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EC</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">EC</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">ED</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">ED</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">EC</font> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> )
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><b>then </b><i><font color="Green">E206</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">EC</font> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
<br/>.= 
<font color="Maroon">EC</font>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_14"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_2_1_14"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EC</font></span>)</span>
 ;<br/><a NAME="E2:74_2_1_14"/><b>then </b><i><font color="Green">E207</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EC</font>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_14_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_14_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_2_1_14_1_1"/>
(  not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_14_1_1_1"><b>suppose </b></a><a NAME="E1:74_2_1_14_1_1_1"/>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_14_1_1_1"/><b>then </b><i><font color="Green">E208</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">E2</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E2</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E2</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_14_1_1_2"><b>suppose </b></a><a NAME="E1:74_2_1_14_1_1_2"/><i><font color="Green">E210</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_14_1_1_2"/><b>then </b>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">E2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E2</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:74_2_1_14"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EC</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E2</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/></div><b>end;</b></div><a NAME="E54:74_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EC</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E2</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E55:74_2_1"/><b>then </b>
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EC</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_004.html#T3">GLIB_004:3</a></i>;<br/><a NAME="E56:74_2_1"/><b>then </b><i><font color="Green">E211</font></i>: 
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EC</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 ;<br/><i><font color="Green">E212</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">ED</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">ED</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
<br/>.= 
<font color="Maroon">EC</font>
<b>by </b><i><a class="ref" href="xboole_1.html#T6">XBOOLE_1:6</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_16"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_2_1_16"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EC</font></span>)</span>
 ;<br/><a NAME="E2:74_2_1_16"/><b>then </b><i><font color="Green">E213</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EC</font>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_16_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_16_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_2_1_16_1_1"/>
(  not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font> or <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_16_1_1_1"><b>suppose </b></a><a NAME="E1:74_2_1_16_1_1_1"/>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>
 ;<br/><div class="add"><a NAME="E2:74_2_1_16_1_1_1"/><b>then </b><i><font color="Green">E214</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ED</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">ED</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">ED</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_16_1_1_2"><b>suppose </b></a><a NAME="E1:74_2_1_16_1_1_2"/><i><font color="Green">E215</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>
 ;<br/><div class="add"><a NAME="E2:74_2_1_16_1_1_2"/><b>then </b>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ED</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">ED</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:74_2_1_16"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EC</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">ED</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/></div><b>end;</b></div><a NAME="E59:74_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EC</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">ED</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E60:74_2_1"/><b>then </b><i><font color="Green">E216</font></i>: 
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EC</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D3" target="_self">Def3</a>, <a class="ref" href="glib_004.html#T3">GLIB_004:3</a></i>;<br/><b>set </b><font color="Maroon">EXXe</font> = <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>;<br/><b>set </b><font color="Maroon">EXXf</font> = <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_17"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:74_2_1_17_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 ;<br/><a NAME="E2:74_2_1_17_1"/><b>then </b>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> &amp; not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E3:74_2_1_17_1"/><b>then </b><i><font color="Green">E217</font></i>: 
( <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font> &amp; not <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E4:74_2_1_17_1"/><b>then </b><i><font color="Green">E218</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E5:74_2_1_17_1"/><b>then </b><i><font color="Green">E219</font></i>: 
not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E6:74_2_1_17_1"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> &amp; not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E7:74_2_1_17_1"/><b>then </b>
not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E8:74_2_1_17_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E9:74_2_1_17_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E10:74_2_1_17_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:74_2_1_17"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E3:74_2_1_17"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E4:74_2_1_17"/><b>then </b><i><font color="Green">E220</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E5:74_2_1_17"/><b>then </b><i><font color="Green">E221</font></i>: 
( <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> &amp; not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:74_2_1_17"/><b>then </b>
not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E7:74_2_1_17"/><b>then </b>
not <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E8:74_2_1_17"/><b>then </b><i><font color="Green">E222</font></i>: 
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E9:74_2_1_17"/>
not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E10:74_2_1_17"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E11:74_2_1_17"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E12:74_2_1_17"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><b>hence </b><a NAME="E13:74_2_1_17"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div><a NAME="E62:74_2_1"/><b>then </b><i><font color="Green">E223</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><b>reconsider </b><font color="Maroon">EV1Xdb</font> = <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font></span>)</span> ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_18"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_2_1_18"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:74_2_1_18"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_2_1_18"/><b>then </b><i><font color="Green">E224</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_2_1_18"/>
not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E5:74_2_1_18"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:74_2_1_18"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E7:74_2_1_18"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div><b>end;</b></div><a NAME="E65:74_2_1"/><b>then </b><i><font color="Green">E225</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/><a NAME="E66:74_2_1"/><i><font color="Green">E226</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EV1Xdb</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> )
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><b>then </b><i><font color="Green">E227</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_20"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_2_1_20"/><i><font color="Green">E228</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:74_2_1_20"/><b>then </b><i><font color="Green">E231</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_20_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_20_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_2_1_20_1_1"/>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> or  not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_20_1_1_1"><b>suppose </b></a><a NAME="E1:74_2_1_20_1_1_1"/><i><font color="Green">E232</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_20_1_1_1"/><b>then </b>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EV1Xdb</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EV1Xdb</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_20_1_1_2"><b>suppose </b></a><a NAME="E1:74_2_1_20_1_1_2"/>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_20_1_1_2"/><b>then </b><i><font color="Green">E233</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EV1Xdb</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EV1Xdb</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EV1Xdb</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:74_2_1_20"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EV1Xdb</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D7" target="_self">Def7</a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/></div><b>end;</b></div><a NAME="E69:74_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E70:74_2_1"/><b>then </b><i><font color="Green">E234</font></i>: 
<span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="glib_004.html#T3">GLIB_004:3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_21"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:74_2_1_21_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span>
 ;<br/><a NAME="E2:74_2_1_21_1"/><b>then </b>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> &amp; not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E3:74_2_1_21_1"/><b>then </b><i><font color="Green">E235</font></i>: 
( <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font> &amp; not <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>,<font color="Maroon">G</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E4:74_2_1_21_1"/><b>then </b><i><font color="Green">E237</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E5:74_2_1_21_1"/><b>then </b><i><font color="Green">E238</font></i>: 
not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E6:74_2_1_21_1"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> &amp; not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E7:74_2_1_21_1"/><b>then </b>
not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D8" target="_self">Def8</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E8:74_2_1_21_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E9:74_2_1_21_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E10:74_2_1_21_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:74_2_1_21"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E3:74_2_1_21"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E4:74_2_1_21"/><b>then </b><i><font color="Green">E240</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V1</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E5:74_2_1_21"/><b>then </b><i><font color="Green">E241</font></i>: 
( <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> &amp; not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:74_2_1_21"/><b>then </b>
not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E7:74_2_1_21"/><b>then </b>
not <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E8:74_2_1_21"/><b>then </b><i><font color="Green">E244</font></i>: 
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E9:74_2_1_21"/>
not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E10:74_2_1_21"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E11:74_2_1_21"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E12:74_2_1_21"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><b>hence </b><a NAME="E13:74_2_1_21"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D8" target="_self">Def8</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div><a NAME="E72:74_2_1"/><b>then </b><i><font color="Green">E245</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><b>reconsider </b><font color="Maroon">EXV1cb</font> = <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font></span>)</span> ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_22"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_2_1_22"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>
 ;<br/><a NAME="E2:74_2_1_22"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E3:74_2_1_22"/><b>then </b><i><font color="Green">E246</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E4:74_2_1_22"/>
not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E5:74_2_1_22"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:74_2_1_22"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E7:74_2_1_22"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div><b>end;</b></div><a NAME="E75:74_2_1"/><b>then </b><i><font color="Green">E247</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/><a NAME="E76:74_2_1"/><i><font color="Green">E248</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXV1cb</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span> )
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><b>then </b><i><font color="Green">E249</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_24"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_2_1_24"/><i><font color="Green">E250</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:74_2_1_24"/><b>then </b><i><font color="Green">E251</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_24_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_24_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_2_1_24_1_1"/>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font> or  not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_24_1_1_1"><b>suppose </b></a><a NAME="E1:74_2_1_24_1_1_1"/><i><font color="Green">E252</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>
 ;<br/><div class="add"><a NAME="E2:74_2_1_24_1_1_1"/><b>then </b>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EXV1cb</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXV1cb</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_005.html#D8" target="_self">Def8</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_24_1_1_2"><b>suppose </b></a><a NAME="E1:74_2_1_24_1_1_2"/>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font>
 ;<br/><div class="add"><a NAME="E2:74_2_1_24_1_1_2"/><b>then </b><i><font color="Green">E253</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EXV1cb</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D11" target="_self">Def11</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXV1cb</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXV1cb</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_005.html#D8" target="_self">Def8</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:74_2_1_24"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXV1cb</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a>, <a class="ref" href="glib_005.html#D10" target="_self">Def10</a>, <a class="ref" href="glib_005.html#D8" target="_self">Def8</a></i>;<br/></div><b>end;</b></div><a NAME="E79:74_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D8" target="_self">Def8</a>, <a class="ref" href="glib_005.html#D9" target="_self">Def9</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E80:74_2_1"/><b>then </b><i><font color="Green">E254</font></i>: 
<span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">V2</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5">(<span class="default"><font color="Maroon">V2</font> <a href="xboole_0.html#K2">\/</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="glib_004.html#T3">GLIB_004:3</a></i>;<br/><b>reconsider </b><font color="Maroon">x</font> =  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span> as   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> <b>by </b><i/>;<br/><a NAME="E82:74_2_1"/>
( <font color="Maroon">x</font> <a href="glib_000.html#K27">.edgesIn()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">x</font> <a href="glib_000.html#K28">.edgesOut()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> )
 <b>by </b><i><a class="ref" href="glib_000.html#T42">GLIB_000:42</a></i>;<br/><a NAME="E83:74_2_1"/><b>then </b><i><font color="Green">E255</font></i>: 
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, , , , </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_25"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:74_2_1_25_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 ;<br/><a NAME="E2:74_2_1_25_1"/><b>then </b>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> &amp; not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E3:74_2_1_25_1"/><b>then </b><i><font color="Green">E256</font></i>: 
( <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">G</font> &amp; not <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">G</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E4:74_2_1_25_1"/><b>then </b><i><font color="Green">E257</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E5:74_2_1_25_1"/><b>then </b>
not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E6:74_2_1_25_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="glib_005.html#D12" target="_self">Def12</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E7:74_2_1_25_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_005.html#D12" target="_self">Def12</a>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E8:74_2_1_25_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:74_2_1_25"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E3:74_2_1_25"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E4:74_2_1_25"/><b>then </b><i><font color="Green">E258</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E5:74_2_1_25"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> &amp; not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:74_2_1_25"/><b>then </b>
not <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E7:74_2_1_25"/><b>then </b><i><font color="Green">E259</font></i>: 
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E8:74_2_1_25"/>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E9:74_2_1_25"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><b>hence </b><a NAME="E10:74_2_1_25"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D12" target="_self">Def12</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div><a NAME="E85:74_2_1"/><b>then </b><i><font color="Green">E260</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><b>reconsider </b><font color="Maroon">EXXfb</font> = <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font></span>)</span> ;<br/><a NAME="E87:74_2_1"/><i><font color="Green">E261</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#T41">GLIB_000:41</a></i>;<br/><a NAME="E88:74_2_1"/><i><font color="Green">E262</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXfb</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">EXXfb</font> )
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><b>then </b><i><font color="Green">E263</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXfb</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">EXXfb</font>
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="glib_005.html#D12" target="_self">Def12</a>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_27"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_2_1_27"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:74_2_1_27"/><b>then </b><i><font color="Green">E264</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_27_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_27_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_2_1_27_1_1"/>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> or  not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_27_1_1_1"><b>suppose </b></a><a NAME="E1:74_2_1_27_1_1_1"/><i><font color="Green">E265</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_27_1_1_1"/><b>then </b>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EXXfb</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXfb</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_27_1_1_2"><b>suppose </b></a><a NAME="E1:74_2_1_27_1_1_2"/>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_27_1_1_2"/><b>then </b><i><font color="Green">E266</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EXXfb</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXfb</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXfb</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:74_2_1_27"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXfb</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/></div><b>end;</b></div><a NAME="E91:74_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXfb</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E92:74_2_1"/><b>then </b><i><font color="Green">E267</font></i>: 
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>,<span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="glib_004.html#T3">GLIB_004:3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_28"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:74_2_1_28_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 ;<br/><a NAME="E2:74_2_1_28_1"/><b>then </b>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> &amp; not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E3:74_2_1_28_1"/><b>then </b><i><font color="Green">E268</font></i>: 
( <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>, <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>,<font color="Maroon">G</font> &amp; not <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">G</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E4:74_2_1_28_1"/><b>then </b><i><font color="Green">E269</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E5:74_2_1_28_1"/><b>then </b>
not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E6:74_2_1_28_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E7:74_2_1_28_1"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E8:74_2_1_28_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:74_2_1_28"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 ;<br/><a NAME="E3:74_2_1_28"/><b>then </b>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E4:74_2_1_28"/><b>then </b><i><font color="Green">E270</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E5:74_2_1_28"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> &amp; not <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:74_2_1_28"/><b>then </b>
not <font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E7:74_2_1_28"/><b>then </b><i><font color="Green">E271</font></i>: 
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><a NAME="E8:74_2_1_28"/>
<font color="Maroon">e</font> <a href="glib_000.html#R4">DSJoins</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>, <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D18">GLIB_000:def 18</a></i>;<br/><a NAME="E9:74_2_1_28"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#D33">GLIB_000:def 33</a></i>;<br/><b>hence </b><a NAME="E10:74_2_1_28"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div><a NAME="E94:74_2_1"/><b>then </b><i><font color="Green">E272</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><b>reconsider </b><font color="Maroon">EXXeb</font> = <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font></span>)</span> ;<br/><a NAME="E96:74_2_1"/><i><font color="Green">E273</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#T41">GLIB_000:41</a></i>;<br/><a NAME="E97:74_2_1"/><i><font color="Green">E274</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXeb</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">EXXeb</font> )
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><b>then </b><i><font color="Green">E275</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXeb</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">EXXeb</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_30"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_2_1_30"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:74_2_1_30"/><b>then </b><i><font color="Green">E276</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2_1_30_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_30_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_2_1_30_1_1"/>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> or  not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_30_1_1_1"><b>suppose </b></a><a NAME="E1:74_2_1_30_1_1_1"/><i><font color="Green">E277</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_30_1_1_1"/><b>then </b>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EXXeb</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXeb</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_2_1_30_1_1_2"><b>suppose </b></a><a NAME="E1:74_2_1_30_1_1_2"/>
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/><div class="add"><a NAME="E2:74_2_1_30_1_1_2"/><b>then </b><i><font color="Green">E278</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">EXXeb</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXeb</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXeb</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:74_2_1_30"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXeb</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/></div><b>end;</b></div><a NAME="E100:74_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">EXXeb</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E101:74_2_1"/><b>then </b>
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><span class="p0">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="glib_004.html#T3">GLIB_004:3</a></i>;<br/><a NAME="E102:74_2_1"/><b>then </b><i><font color="Green">E279</font></i>: 
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">sink</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D11" target="_self">Def11</a>, </i>;<br/><a NAME="E103:74_2_1"/>
<span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <font color="Maroon">E2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_005.html#K2" target="_self">.flow</a> <font color="Maroon">source</font>,<font color="Maroon">sink</font>
 <b>by </b><i>, , , , , <a class="ref" href="glib_005.html#D7" target="_self">Def7</a>, <a class="ref" href="glib_005.html#D10" target="_self">Def10</a>, </i>;<br/><b>hence </b><a NAME="E104:74_2_1"/>
<font color="Maroon">G</font> <a href="glib_005.html#K2" target="_self">.flow</a> <font color="Maroon">source</font>,<font color="Maroon">sink</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V2</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V2</font></span>)</span>,<font color="Maroon">V2</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:74_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div>
<a NAME="E5:74"/><i><font color="Green">E280</font></i>: 
for <font color="Olive">n</font> being non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">n</font>]
 
<b>from </b><i><a class="ref" href="binarith.html#S1">BINARITH:sch 1</a>(, );<br/></i>
<b>set </b><font color="Maroon">n</font> =  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:74_3"/>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E2:74_3"/><b>then </b><i><font color="Green">E281</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="card_2.html#T59">CARD_2:59</a></i>;<br/><a NAME="E3:74_3"/>
<font color="Maroon">sink</font> is   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:74_3"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:74"/>
<font color="Maroon">G</font> <a href="glib_005.html#K2" target="_self">.flow</a> <font color="Maroon">source</font>,<font color="Maroon">sink</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <font color="Maroon">V</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K24">.edgesDBetween</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">V</font></span>)</span>,<font color="Maroon">V</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/>


</div>
