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<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#V2" title="GLIB_000:attr.2">_finite</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a>  is  <a href="lexbfs.html#V6" title="LEXBFS:attr.6">with_property_T</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">CS</font> =  <a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">L</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> ;<br/>
<a NAME="E1:136"/><span class="lab"><font color="Green" title="E98">A1</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a>  is  <a href="lexbfs.html#V5" title="LEXBFS:attr.5">with_property_L3</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lexbfs.html#T53" target="_self" onmouseover="rs('lexbfs/T53')" onmouseout="rh()">Th53</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="136_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> &amp; <font color="Olive" title="b2">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> &amp; <font color="Olive" title="b3">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">b</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">b</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  &amp;  not <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  holds <br/> ex <font color="Olive" title="b4">d</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b4">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">b</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  &amp;  not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">d</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  )</span></a><div class="add"><span class="kw">let </span><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 <font color="Maroon" title="c1">G</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> &amp; <font color="Maroon" title="c5">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> &amp; <font color="Maroon" title="c6">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></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>  implies  ex <font color="Olive" title="b1">d</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b1">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c5">b</font>,<font color="Olive" title="b1">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="Olive" title="b1">d</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  ) )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:136_1"/><span class="lab"><font color="Green" title="E99">A2</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:136_1"/><span class="lab"><font color="Green" title="E100">A3</font></span>: 
<font color="Maroon" title="c5">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:136_1"/><span class="lab"><font color="Green" title="E101">A4</font></span>: 
<font color="Maroon" title="c6">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:136_1"/><span class="lab"><font color="Green" title="E102">A5</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c5">b</font>
 <span class="kw">and </span><br/><a NAME="E5:136_1"/><span class="lab"><font color="Green" title="E103">A6</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c6">c</font>
 <span class="kw">and </span><br/><a NAME="E6:136_1"/><span class="lab"><font color="Green" title="E104">A7</font></span>: 
<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> 
 <span class="kw">and </span><br/><a NAME="E7:136_1"/><span class="lab"><font color="Green" title="E105">A8</font></span>: 
 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> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">d</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b1">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c5">b</font>,<font color="Olive" title="b1">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="Olive" title="b1">d</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  )</span><br/><span class="kw">consider </span><font color="Maroon" title="c7">d</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E9:136_1"/><span class="lab"><font color="Green" title="E106">A9</font></span>: 
<font color="Maroon" title="c7">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E10:136_1"/><span class="lab"><font color="Green" title="E107">A10</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">d</font>
 <span class="kw">and </span><br/><a NAME="E11:136_1"/><span class="lab"><font color="Green" title="E108">A11</font></span>: 
<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> 
 <span class="kw">and </span><br/><a NAME="E12:136_1"/><span class="lab"><font color="Green" title="E109">A12</font></span>: 
 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> 
 <span class="kw">and </span><br/><a NAME="E13:136_1"/>
 for <font color="Olive" title="b1">e</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:136"><span class="lab"><font color="Green" title="E98">A1</font></span></a>, <a class="txt" href="#E1:136_1"><span class="lab"><font color="Green" title="E99">A2</font></span></a>, <a class="txt" href="#E2:136_1"><span class="lab"><font color="Green" title="E100">A3</font></span></a>, <a class="txt" href="#E3:136_1"><span class="lab"><font color="Green" title="E101">A4</font></span></a>, <a class="txt" href="#E4:136_1"><span class="lab"><font color="Green" title="E102">A5</font></span></a>, <a class="txt" href="#E5:136_1"><span class="lab"><font color="Green" title="E103">A6</font></span></a>, <a class="txt" href="#E6:136_1"><span class="lab"><font color="Green" title="E104">A7</font></span></a>, <a class="txt" href="#E7:136_1"><span class="lab"><font color="Green" title="E105">A8</font></span></a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c8">d</font> = <font color="Maroon" title="c7">d</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c8">d</font> &amp; <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>  &amp;  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>  )</span><br/><span class="kw">thus </span><a NAME="E14:136_1"/>
<font color="Maroon" title="c8">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:136_1"><span class="lab"><font color="Green" title="E106">A9</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c8">d</font> &amp; <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>  &amp;  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>  )</span><br/><span class="kw">thus </span><a NAME="E15:136_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c8">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:136_1"><span class="lab"><font color="Green" title="E103">A6</font></span></a>, <a class="txt" href="#E10:136_1"><span class="lab"><font color="Green" title="E107">A10</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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>  &amp;  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>  )</span><br/><span class="kw">thus </span><a NAME="E16:136_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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:136_1"><span class="lab"><font color="Green" title="E108">A11</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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> </span><br/><span class="kw">thus </span><a NAME="E17:136_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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:136_1"><span class="lab"><font color="Green" title="E109">A12</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:136"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K14" title="LEXBFS:func.14">.Result()</a></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a>  is  <a href="lexbfs.html#V6" title="LEXBFS:attr.6">with_property_T</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
