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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>

<b>set </b><font color="Maroon" title="c2">CS</font> =  <a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font>;<br/>
<b>set </b><font color="Maroon" title="c3">G</font> = <span class="p1">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> ;<br/>
<a NAME="E1:219"/><i><font color="Green" title="E127">A1</font></i>: 
<span class="p1">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a>  is <a href="lexbfs.html#V21" title="LEXBFS:attr.21">with_property_L3</a>
 
<b>by </b><i><a class="ref" href="lexbfs.html#T65" target="_self" title="LEXBFS:th.65">Th65</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="219_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c6">c</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span>;<br/><b>assume </b><a NAME="E1:219_1"/><i><font color="Green" title="E128">A2</font></i>: 
( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c4">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c5">b</font> &amp; <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c5">b</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c6">c</font> &amp; <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">c</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  &amp; not <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">c</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  )
 ;<br/><b>consider </b><font color="Maroon" title="c7">d</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span><b> such that </b><br/><a NAME="E3:219_1"/><i><font color="Green" title="E129">A3</font></i>: 
( <font color="Maroon" title="c7">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c6">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">d</font> &amp; <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">d</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  &amp; not <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c7">d</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  &amp; ( for <font color="Olive" title="b1">e</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span>  st <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font> &amp; <font color="Olive" title="b1">e</font>,<font color="Maroon" title="c5">b</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  &amp; not <font color="Olive" title="b1">e</font>,<font color="Maroon" title="c4">a</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  holds <br/><span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">e</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">d</font> ) )
 <b>by </b><i><a class="txt" href="lexbfs.html#E1:219"><i><font color="Green" title="E127">A1</font></i></a>, <a class="txt" href="lexbfs.html#E1:219_1"><i><font color="Green" title="E128">A2</font></i></a>, <a class="ref" href="lexbfs.html#D34" target="_self" title="LEXBFS:def.34">Def34</a></i>;<br/><b>take </b><font color="Maroon" title="c8">d</font> = <font color="Maroon" title="c7">d</font>;<br/><b>thus </b><a NAME="E4:219_1"/>
<font color="Maroon" title="c8">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E3:219_1"><i><font color="Green" title="E129">A3</font></i></a></i>;<br/><b>thus </b><a NAME="E5:219_1"/>
<span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c5">b</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a> </span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c8">d</font>
 <b>by </b><i><a class="txt" href="lexbfs.html#E1:219_1"><i><font color="Green" title="E128">A2</font></i></a>, <a class="txt" href="lexbfs.html#E3:219_1"><i><font color="Green" title="E129">A3</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><b>thus </b><a NAME="E6:219_1"/>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c8">d</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> 
 <b>by </b><i><a class="txt" href="lexbfs.html#E3:219_1"><i><font color="Green" title="E129">A3</font></i></a></i>;<br/><b>thus </b><a NAME="E7:219_1"/>
not <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c8">d</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> 
 <b>by </b><i><a class="txt" href="lexbfs.html#E3:219_1"><i><font color="Green" title="E129">A3</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:219"/>
<span class="p1">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K19" title="LEXBFS:func.19">.Result()</a>  is <a href="lexbfs.html#V22" title="LEXBFS:attr.22">with_property_T</a>
 <b>by </b><i><a class="ref" href="lexbfs.html#D41" target="_self" title="LEXBFS:def.41">Def41</a></i>;<br/>


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