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<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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/> for <font color="Olive" title="b3">v</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="b2">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><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#K13" title="LEXBFS:func.13">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="lexbfs.html#K17" title="LEXBFS:func.17">.</a> <font color="Olive" title="b3">v</font> holds <br/> ex <font color="Olive" title="b4">w</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">w</font> <a href="hidden.html#R2" title="HIDDEN: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#K13" title="LEXBFS:func.13">.</a> <font color="Olive" title="b1">i</font></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#K13" title="LEXBFS:func.13">.</a> <font color="Olive" title="b1">i</font></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">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">j</font> &amp; <font color="Olive" title="b3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b4">w</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">i</font>, <font color="Maroon" title="c3">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">v</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="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="lexbfs.html#K17" title="LEXBFS:func.17">.</a> <font color="Olive" title="b1">v</font> holds <br/> ex <font color="Olive" title="b2">w</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="b2">w</font> <a href="hidden.html#R2" title="HIDDEN: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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></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">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">j</font> &amp; <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">w</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">v</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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="lexbfs.html#K17" title="LEXBFS:func.17">.</a> <font color="Maroon" title="c4">v</font> implies  ex <font color="Olive" title="b1">w</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">w</font> <a href="hidden.html#R2" title="HIDDEN: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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></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">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">j</font> &amp; <font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">w</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> ) )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c5">CSI</font> = <span class="p1">(<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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">VLI</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#K15" title="LEXBFS:func.15">``1</a> </span>)</span> <a href="lexbfs.html#K5" title="LEXBFS:func.5">.</a> <font color="Maroon" title="c2">i</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">V2I</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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">n</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">CSN</font> = <span class="p1">(<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#K13" title="LEXBFS:func.13">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">VLN</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#K13" title="LEXBFS:func.13">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font></span>)</span></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> ;<br/>
<a NAME="E1:100"/><span class="lab"><font color="Green" title="E75">A1</font></span>: 
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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="glib_000.html#K39" title="GLIB_000:func.39">.Lifespan()</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lexbfs.html#T37" target="_self" title="LEXBFS:th.37">Th37</a></span>;<br/>
<a NAME="E2:100"/><span class="lab"><font color="Green" title="E76">A2</font></span>: 
<span class="p1">(<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="glib_000.html#K39" title="GLIB_000:func.39">.Lifespan()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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#K15" title="LEXBFS:func.15">``1</a> </span>)</span> <a href="glib_000.html#K39" title="GLIB_000:func.39">.Lifespan()</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lexbfs.html#T39" target="_self" title="LEXBFS:th.39">Th39</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:100"/><span class="lab"><font color="Green" title="E77">A3</font></span>: 
<font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="lexbfs.html#K17" title="LEXBFS:func.17">.</a> <font color="Maroon" title="c4">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">w</font> being  <a href="glib_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">w</font> <a href="hidden.html#R2" title="HIDDEN: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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></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">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">j</font> &amp; <font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">w</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">w</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="E5:100"/><span class="lab"><font color="Green" title="E78">A4</font></span>: 
 <a href="lexbfs.html#K10" title="LEXBFS:func.10">LexBFS:PickUnnumbered</a> <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#K13" title="LEXBFS:func.13">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">w</font>
 <span class="kw">and </span><br/><a NAME="E6:100"/>
not <font color="Maroon" title="c11">w</font> <a href="hidden.html#R2" title="HIDDEN: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#K13" title="LEXBFS:func.13">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font></span>)</span></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span>
 <span class="kw">and </span><br/><a NAME="E7:100"/><span class="lab"><font color="Green" title="E79">A5</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c11">w</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lexbfs.html#T48" target="_self" title="LEXBFS:th.48">Th48</a></span>;<br/>
<a NAME="E8:100"/><span class="lab"><font color="Green" title="E80">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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="lexbfs.html#K17" title="LEXBFS:func.17">.</a> <font color="Maroon" title="c4">v</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lexbfs.html#T43" target="_self" title="LEXBFS:th.43">Th43</a></span>;<br/>
<a NAME="E9:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A7</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">j</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:100"><span class="lab"><font color="Green" title="E77">A3</font></span></a>, <a class="ref" href="lexbfs.html#T3" target="_self" title="LEXBFS:th.3">Th3</a></span>;<br/>
<a NAME="E10:100"/><span class="lab"><font color="Green" title="E82">A8</font></span>: 
<font color="Maroon" title="c3">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:100"><span class="lab"><font color="Green" title="E77">A3</font></span></a>, <a class="txt" href="#E8:100"><span class="lab"><font color="Green" title="E80">A6</font></span></a>, <a class="ref" href="lexbfs.html#T3" target="_self" title="LEXBFS:th.3">Th3</a></span>;<br/>
<a NAME="E11:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A9</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">j</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a></span>;<br/>
<a NAME="E12:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A10</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:100"><span class="lab"><font color="Green" title="E81">A7</font></span></a>, <a class="ref" href="xreal_1.html#T46" title="XREAL_1:th.46">XREAL_1:46</a></span>;<br/>
<a NAME="E13:100"/><span class="lab"><font color="Green" title="E85">A11</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:100"><span class="lab"><font color="Green" title="E82">A8</font></span></a>, <a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a></span>;<br/>
<a NAME="E14:100"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:100"><span class="lab"><font color="Green" title="E81">A7</font></span></a>, <a class="ref" href="xreal_0.html#D2" title="XREAL_0:def.2">XREAL_0:def 2</a></span>;<br/>
<a NAME="E15:100"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">i</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"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/>
<a NAME="E16:100"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font></span>)</span> <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"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/>
<a NAME="E17:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A12</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></span>;<br/>
<a NAME="E18:100"/><span class="lab"><font color="Green" title="E87">A13</font></span>: 
<font color="Maroon" title="c11">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K15" title="LEXBFS:func.15">``1</a> </span>)</span> <a href="lexbfs.html#K6" title="LEXBFS:func.6">.PickedAt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:100"><span class="lab"><font color="Green" title="E78">A4</font></span></a>, <a class="txt" href="#E9:100"><span class="lab"><font color="Green" title="E81">A7</font></span></a>, <a class="txt" href="#E11:100"><span class="lab"><font color="Green" title="E83">A9</font></span></a>, <a class="ref" href="lexbfs.html#T41" target="_self" title="LEXBFS:th.41">Th41</a>, <a class="ref" href="xreal_1.html#T46" title="XREAL_1:th.46">XREAL_1:46</a></span>;<br/>
<a NAME="E19:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A14</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#K15" title="LEXBFS:func.15">``1</a> </span>)</span> <a href="lexbfs.html#K5" title="LEXBFS:func.5">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c11">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:100"><span class="lab"><font color="Green" title="E84">A10</font></span></a>, <a class="txt" href="#E1:100"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="txt" href="#E2:100"><span class="lab"><font color="Green" title="E76">A2</font></span></a>, <a class="txt" href="#E17:100"><span class="lab"><font color="Green" title="E86">A12</font></span></a>, <a class="ref" href="lexbfs.html#T21" target="_self" title="LEXBFS:th.21">Th21</a></span>;<br/>
<a NAME="E20:100"/><span class="lab"><font color="Green" title="E89">A15</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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a>  <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <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#K15" title="LEXBFS:func.15">``1</a> </span>)</span> <a href="lexbfs.html#K5" title="LEXBFS:func.5">.</a> <font color="Maroon" title="c2">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lexbfs.html#D16" target="_self" title="LEXBFS:def.16">Def16</a></span>;<br/>
<a NAME="E21:100"/><span class="kw">then </span>
<font color="Maroon" title="c11">w</font> <a href="hidden.html#R2" title="HIDDEN: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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></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="#E12:100"><span class="lab"><font color="Green" title="E84">A10</font></span></a>, <a class="txt" href="#E1:100"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="txt" href="#E2:100"><span class="lab"><font color="Green" title="E76">A2</font></span></a>, <a class="txt" href="#E18:100"><span class="lab"><font color="Green" title="E87">A13</font></span></a>, <a class="txt" href="#E17:100"><span class="lab"><font color="Green" title="E86">A12</font></span></a>, <a class="ref" href="lexbfs.html#T21" target="_self" title="LEXBFS:th.21">Th21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E22:100"/>
 ex <font color="Olive" title="b1">w</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">w</font> <a href="hidden.html#R2" title="HIDDEN: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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></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#K13" title="LEXBFS:func.13">.</a> <font color="Maroon" title="c2">i</font></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">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">j</font> &amp; <font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">w</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:100"><span class="lab"><font color="Green" title="E89">A15</font></span></a>, <a class="txt" href="#E7:100"><span class="lab"><font color="Green" title="E79">A5</font></span></a>, <a class="txt" href="#E12:100"><span class="lab"><font color="Green" title="E84">A10</font></span></a>, <a class="txt" href="#E13:100"><span class="lab"><font color="Green" title="E85">A11</font></span></a>, <a class="txt" href="#E19:100"><span class="lab"><font color="Green" title="E88">A14</font></span></a>, <a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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