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<div class="add">

<b>let </b><font color="Maroon">G</font> be  <a href="glib_000.html#V2">finite</a> <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>set </b><font color="Maroon">CN</font> = <span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font>;<br/>
<b>set </b><font color="Maroon">VLN</font> =  <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="218_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be   <a href="glib_000.html#NM10">Vertex</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">b</font> be   <a href="glib_000.html#NM10">Vertex</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">c</font> be   <a href="glib_000.html#NM10">Vertex</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:218_1"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> )
 <b>and </b><br/><a NAME="E2:218_1"/><i><font color="Green">E36</font></i>: 
( <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font> &amp; <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c</font> )
 <b>and </b><br/><a NAME="E3:218_1"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="chord.html#R1">are_adjacent</a>  &amp; not <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="chord.html#R1">are_adjacent</a>  )
 ;<br/><a NAME="E4:218_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#R5">==</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font>
 <b>by </b><i/>;<br/><a NAME="E5:218_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> 
 <b>by </b><i/>;<br/><a NAME="E6:218_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="glib_003.html#K14">.labeledV()</a>  &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="glib_003.html#K14">.labeledV()</a>  &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="glib_003.html#K14">.labeledV()</a>  )
 <b>by </b><i><a class="txt" href="lexbfs.html#E19"><i><font color="Green">Lemma127</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="218_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:218_1_1"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">d</font> being  <a href="glib_000.html#NM10">Vertex</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span>  st <font color="Olive">d</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Olive">d</font> &amp; <font color="Maroon">b</font>,<font color="Olive">d</font> <a href="chord.html#R1">are_adjacent</a>  holds <br/><font color="Maroon">a</font>,<font color="Olive">d</font> <a href="chord.html#R1">are_adjacent</a> 
 ;<br/><b>set </b><font color="Maroon">bn</font> = <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span>;<br/><b>set </b><font color="Maroon">CSB</font> = <span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">VLB</font> =  <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">VL2</font> =  <a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span>;<br/><a NAME="E2:218_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E3:218_1_1"/><b>then </b>
 <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E2"><i><font color="Green">Lemma52</font></i></a></i>;<br/><a NAME="E4:218_1_1"/><b>then </b><i><font color="Green">E46</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T25">RELAT_1:25</a></i>;<br/><a NAME="E5:218_1_1"/>
<span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> 
 <b>by </b><i>, <a class="txt" href="lexbfs.html#E10:218_1_1"><i><font color="Green">E50</font></i></a></i>;<br/><a NAME="E6:218_1_1"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</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#K16">.order()</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E7:218_1_1"/><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> 
 <b>by </b><i><a class="ref" href="binarith.html#T52">BINARITH:52</a></i>;<br/><a NAME="E8:218_1_1"/>
<span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E9:218_1_1"/><b>then </b><i><font color="Green">E49</font></i>: 
<span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="lexbfs.html#D7" target="_self">Def7</a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E10:218_1_1"/><i><font color="Green">E50</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E11:218_1_1"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="txt" href="lexbfs.html#E10:218_1_1"><i><font color="Green">E50</font></i></a></i>;<br/><a NAME="E12:218_1_1"/><b>then </b><i><font color="Green">E51</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> 
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T46">XREAL_1:46</a></i>;<br/><a NAME="E13:218_1_1"/><b>then </b><i><font color="Green">E89</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E14:218_1_1"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K10" target="_self">.PickedAt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/><a NAME="E15:218_1_1"/><b>then </b><i><font color="Green">E91</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="lexbfs.html#K21" target="_self">MCS:PickUnnumbered</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="218_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:218_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:218_1_1_1"/><b>then </b><i><font color="Green">E92</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> 
 ;<br/><a NAME="E3:218_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="lexbfs.html#D9" target="_self">Def9</a>, , </i>;<br/><b>hence </b><a NAME="E4:218_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="lexbfs.html#E20"><i><font color="Green">Lemma128</font></i></a>, <a class="ref" href="lexbfs.html#T11" target="_self">Th11</a>, , </i>;<br/></div><b>end;</b></div><a NAME="E17:218_1_1"/><b>then </b><i><font color="Green">E93</font></i>: 
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">a</font>
 <b>by </b><i>, , , </i>;<br/><a NAME="E18:218_1_1"/>
not <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, , , </i>;<br/><a NAME="E19:218_1_1"/><b>then </b><i><font color="Green">E94</font></i>: 
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E20:218_1_1"/>
not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> 
 <b>by </b><i>, , <a class="txt" href="lexbfs.html#E20"><i><font color="Green">Lemma128</font></i></a>, <a class="ref" href="lexbfs.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E21:218_1_1"/><b>then </b><i><font color="Green">E95</font></i>: 
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E22:218_1_1"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> 
 <b>by </b><i>, , <a class="txt" href="lexbfs.html#E20"><i><font color="Green">Lemma128</font></i></a>, </i>;<br/><a NAME="E23:218_1_1"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="chord.html#K2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E20"><i><font color="Green">Lemma128</font></i></a>, , <a class="ref" href="chord.html#T52">CHORD:52</a></i>;<br/><a NAME="E24:218_1_1"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="chord.html#T51">CHORD:51</a></i>;<br/><a NAME="E25:218_1_1"/><b>then </b><i><font color="Green">E97</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E26:218_1_1"/>
not <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="chord.html#K2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="chord.html#T52">CHORD:52</a></i>;<br/><a NAME="E27:218_1_1"/><b>then </b>
not <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="chord.html#T51">CHORD:51</a></i>;<br/><a NAME="E28:218_1_1"/><b>then </b><i><font color="Green">E98</font></i>: 
not <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="218_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:218_1_1_2"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:218_1_1_2"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="lexbfs.html#D13" target="_self">Def13</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E3:218_1_1_2"/><b>then </b><i><font color="Green">E101</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E4:218_1_1_2"/><i><font color="Green">E102</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> 
 <b>by </b><i><a class="ref" href="lexbfs.html#D13" target="_self">Def13</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E5:218_1_1_2"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_003.html#T7">GLIB_003:7</a></i>;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as   <a href="glib_000.html#NM10">Vertex</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <b>by </b><i><a class="ref" href="lexbfs.html#T13" target="_self">Th13</a></i>;<br/><b>set </b><font color="Maroon">CSB1</font> = <span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/><b>set </b><font color="Maroon">VLB1</font> =  <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>;<br/><a NAME="E7:218_1_1_2"/>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> 
 <b>by </b><i>, , , <a class="txt" href="lexbfs.html#E6:218_1_1"><i><font color="Green">E47</font></i></a></i>;<br/><a NAME="E8:218_1_1_2"/><b>then </b><i><font color="Green">E103</font></i>: 
( <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font> &amp; <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">d</font> )
 <b>by </b><i>, , , </i>;<br/><a NAME="E9:218_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T41">XREAL_1:41</a></i>;<br/><a NAME="E10:218_1_1_2"/><b>then </b>
 <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E2"><i><font color="Green">Lemma52</font></i></a></i>;<br/><a NAME="E11:218_1_1_2"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T25">RELAT_1:25</a></i>;<br/><a NAME="E12:218_1_1_2"/><b>then </b>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> 
 <b>by </b><i/>;<br/><a NAME="E13:218_1_1_2"/><b>then </b><i><font color="Green">E104</font></i>: 
<span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">d</font>
 <b>by </b><i>, </i>;<br/><a NAME="E14:218_1_1_2"/>
<span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><a NAME="E15:218_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.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#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="txt" href="lexbfs.html#E9:218_1_1"><i><font color="Green">E49</font></i></a></i>;<br/><a NAME="E16:218_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">d</font>
 <b>by </b><i>, </i>;<br/><a NAME="E17:218_1_1_2"/><b>then </b><i><font color="Green">E116</font></i>: 
<span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">d</font>
 <b>by </b><i>, , , , , <a class="txt" href="lexbfs.html#E7:218_1_1"><i><font color="Green">E48</font></i></a></i>;<br/><a NAME="E18:218_1_1_2"/>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="lexbfs.html#D13" target="_self">Def13</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E19:218_1_1_2"/><b>then </b>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="chord.html#K2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="chord.html#T51">CHORD:51</a></i>;<br/><a NAME="E20:218_1_1_2"/><b>then </b>
( <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> &amp; <font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="chord.html#R1">are_adjacent</a>  )
 <b>by </b><i><a class="ref" href="chord.html#T52">CHORD:52</a></i>;<br/><a NAME="E21:218_1_1_2"/><b>then </b><i><font color="Green">E117</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="chord.html#R1">are_adjacent</a> 
 <b>by </b><i>, , , </i>;<br/><a NAME="E22:218_1_1_2"/>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="chord.html#K2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="chord.html#T52">CHORD:52</a>, , <a class="txt" href="lexbfs.html#E20"><i><font color="Green">Lemma128</font></i></a></i>;<br/><a NAME="E23:218_1_1_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="chord.html#T51">CHORD:51</a></i>;<br/><b>hence </b><a NAME="E24:218_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><a NAME="E30:218_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</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="chord.html#K2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/><a NAME="E31:218_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R2">c&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">G</font> <a href="glib_000.html#K16">.order()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="lexbfs.html#D11" target="_self">Def11</a>, <a class="ref" href="lexbfs.html#D12" target="_self">Def12</a>, <a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/><b>hence </b><a NAME="E32:218_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="lexbfs.html#T11" target="_self">Th11</a>, <a class="ref" href="lexbfs.html#T12" target="_self">Th12</a>, , <a class="ref" href="trees_1.html#T24">TREES_1:24</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:218_1"/>
 ex <font color="Olive">d</font> being  <a href="glib_000.html#NM10">Vertex</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span> st <br/>( <font color="Olive">d</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">b</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Olive">d</font> &amp; <font color="Maroon">b</font>,<font color="Olive">d</font> <a href="chord.html#R1">are_adjacent</a>  &amp; not <font color="Maroon">a</font>,<font color="Olive">d</font> <a href="chord.html#R1">are_adjacent</a>  )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:218"/>
<span class="p1">(<span class="default"><a href="lexbfs.html#K26" target="_self">MCS:CSeq</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K9" target="_self">.</a> <font color="Maroon">n</font> is <a href="lexbfs.html#V22" target="_self">with_property_T</a>
 <b>by </b><i><a class="txt" href="lexbfs.html#E18"><i><font color="Green">Lemma126</font></i></a></i>;<br/>


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