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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">n</font>, <font color="Maroon" title="c4">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:170"/><i><font color="Green" title="E91">A1</font></i>: 
<font color="Maroon" title="c4">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">n</font>
 <b>and </b><br/><a NAME="E2:170"/><i><font color="Green" title="E92">A2</font></i>: 
<font color="Maroon" title="c3">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">m</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c5">CSN</font> = <span class="p1">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <font color="Maroon" title="c3">n</font>;<br/>
<b>set </b><font color="Maroon" title="c6">V2N</font> =  <a href="lexbfs.html#K6" title="LEXBFS:func.6">the_V2Label_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <font color="Maroon" title="c3">n</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c7">CSM</font> = <span class="p1">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <font color="Maroon" title="c2">m</font>;<br/>
<b>set </b><font color="Maroon" title="c8">V2M</font> =  <a href="lexbfs.html#K6" title="LEXBFS:func.6">the_V2Label_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <font color="Maroon" title="c2">m</font></span>)</span>;<br/>
<b>let </b><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E3:170"/><i><font color="Green" title="E93">A3</font></i>: 
not <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" title="LEXBFS:func.6">the_V2Label_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span> <a href="lexbfs.html#K2" title="LEXBFS:func.2">.</a> <font color="Maroon" title="c9">x</font>
 ;<br/>

<a NAME="E4:170"/>
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" title="LEXBFS:func.6">the_V2Label_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span> <a href="lexbfs.html#K2" title="LEXBFS:func.2">.</a> <font color="Maroon" title="c9">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a> </span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lexbfs.html#T55" target="_self" title="LEXBFS:th.55">Th55</a></i>;<br/>
<b>set </b><font color="Maroon" title="c10">CSK</font> = <span class="p1">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <font color="Maroon" title="c4">k</font>;<br/>
<b>set </b><font color="Maroon" title="c11">V2K</font> =  <a href="lexbfs.html#K6" title="LEXBFS:func.6">the_V2Label_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <font color="Maroon" title="c4">k</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c12">CK1</font> = <span class="p1">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c13">V21</font> =  <a href="lexbfs.html#K6" title="LEXBFS:func.6">the_V2Label_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>;<br/>
<a NAME="E5:170"/>
<font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">n</font>
 
<b>by </b><i><a class="txt" href="lexbfs.html#E1:170"><i><font color="Green" title="E91">A1</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E6:170"/><b>then </b>
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" title="LEXBFS:func.6">the_V2Label_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="lexbfs.html#K2" title="LEXBFS:func.2">.</a> <font color="Maroon" title="c9">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" title="LEXBFS:func.6">the_V2Label_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span> <a href="lexbfs.html#K2" title="LEXBFS:func.2">.</a> <font color="Maroon" title="c9">x</font>
 
<b>by </b><i><a class="ref" href="lexbfs.html#T56" target="_self" title="LEXBFS:th.56">Th56</a></i>;<br/>
<a NAME="E7:170"/><b>then </b><i><font color="Green" title="E94">A6</font></i>: 
not <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" title="LEXBFS:func.6">the_V2Label_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="lexbfs.html#K2" title="LEXBFS:func.2">.</a> <font color="Maroon" title="c9">x</font>
 
<b>by </b><i><a class="txt" href="lexbfs.html#E3:170"><i><font color="Green" title="E93">A3</font></i></a></i>;<br/>
<a NAME="E8:170"/>
<font color="Maroon" title="c4">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">m</font>
 
<b>by </b><i><a class="txt" href="lexbfs.html#E1:170"><i><font color="Green" title="E91">A1</font></i></a>, <a class="txt" href="lexbfs.html#E2:170"><i><font color="Green" title="E92">A2</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E9:170"/>
not <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" title="LEXBFS:func.6">the_V2Label_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K18" title="LEXBFS:func.18">LexBFS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K9" title="LEXBFS:func.9">.</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span> <a href="lexbfs.html#K2" title="LEXBFS:func.2">.</a> <font color="Maroon" title="c9">x</font>
 <b>by </b><i><a class="txt" href="lexbfs.html#E7:170"><i><font color="Green" title="E94">A6</font></i></a>, <a class="ref" href="lexbfs.html#T58" target="_self" title="LEXBFS:th.58">Th58</a></i>;<br/>


</div>
