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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a>  holds <br/> ex <font color="Olive" title="b2">w</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Olive" title="b1">n</font></span>)</span> &amp; ( for <font color="Olive" title="b3">v</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( ( <font color="Olive" title="b3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">w</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; not <font color="Olive" title="b3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b3">v</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 ) &amp; ( (  not <font color="Olive" title="b3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">w</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> or <font color="Olive" title="b3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> ) implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b3">v</font> ) ) ) )</span><br/><b>let </b><font color="Maroon" title="c2">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a>  implies  ex <font color="Olive" title="b1">w</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b1">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> &amp; ( for <font color="Olive" title="b2">v</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( ( <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">w</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; not <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 ) &amp; ( (  not <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">w</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> or <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> ) implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">v</font> ) ) ) ) )</span><br/>



<b>assume </b><a NAME="E1:138"/><i><font color="Green" title="E103">A1</font></i>: 
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">w</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b1">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> &amp; ( for <font color="Olive" title="b2">v</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( ( <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">w</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; not <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 ) &amp; ( (  not <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">w</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> or <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> ) implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">v</font> ) ) ) )</span><br/>

<b>set </b><font color="Maroon" title="c3">CSN</font> = <span class="p1">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font>;<br/>
<b>set </b><font color="Maroon" title="c4">VLN</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> ;<br/>
<b>set </b><font color="Maroon" title="c5">V2N</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> ;<br/>
<b>set </b><font color="Maroon" title="c6">CN1</font> = <span class="p1">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c7">V21</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> ;<br/>
<b>set </b><font color="Maroon" title="c8">w</font> =  <a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c9">k</font> = <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="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">n</font>;<br/>
<a NAME="E2:138"/><i><font color="Green" title="E104">A2</font></i>: 
<font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:138"><i><font color="Green" title="E103">A1</font></i></a>, <a class="ref" href="lexbfs.html#T65" target="_self" title="LEXBFS:th.65">Th82</a></i>;<br/>
<b>set </b><font color="Maroon" title="c10">CSlv</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<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="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c11">CSlv1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</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="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>;<br/>
<a NAME="E3:138"/><i><font color="Green" title="E105">d1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="lexbfs.html#E2"><i><font color="Green" title="E2">Tw0</font></i></a></i>;<br/>
<a NAME="E4:138"/><i><font color="Green" title="E106">r1</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T18" title="FUNCT_4:th.18">FUNCT_4:18</a></i>;<br/>
<a NAME="E5:138"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</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="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">n</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a></i>;<br/>
<a NAME="E6:138"/><b>then </b>
<span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E7:138"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a> </span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="txt" href="#E4:138"><i><font color="Green" title="E106">r1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E8:138"/><b>then </b><i><font color="Green" title="E107">A2a</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</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="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rfunct_3.html#K4" title="RFUNCT_3:func.4">PFuncs</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="txt" href="#E3:138"><i><font color="Green" title="E105">d1</font></i></a>, <a class="ref" href="partfun1.html#D5" title="PARTFUN1:def.5">PARTFUN1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">CSlv</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<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="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as   <a href="lexbfs.html#NM5" title="LEXBFS:NM.5">MCS:Labeling</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="txt" href="#E8:138"><i><font color="Green" title="E107">A2a</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<i><font color="Green" title="E108">A5</font></i>: <span class="p1">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="lexbfs.html#K22" title="LEXBFS:func.22">MCS:Step</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span>
<b>by </b><i><a class="ref" href="lexbfs.html#D26" target="_self" title="LEXBFS:def.26">Def40</a></i>
<br/>.= 
 <a href="lexbfs.html#K21" title="LEXBFS:func.21">MCS:Update</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">n</font>
<b>by </b><i><a class="txt" href="#E1:138"><i><font color="Green" title="E103">A1</font></i></a>, <a class="txt" href="#E2:138"><i><font color="Green" title="E104">A2</font></i></a>, <a class="ref" href="lexbfs.html#D23" target="_self" title="LEXBFS:def.23">Def39</a></i>
<br/>.= 
 <a href="lexbfs.html#K20" title="LEXBFS:func.20">MCS:LabelAdjacent</a> <font color="Maroon" title="c12">CSlv</font>,<span class="p1">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lexbfs.html#D22" target="_self" title="LEXBFS:def.22">dLMCSU</a></i>
;<br/>
<b>set </b><font color="Maroon" title="c13">VLv</font> = <font color="Maroon" title="c12">CSlv</font> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> ;<br/>
<b>set </b><font color="Maroon" title="c14">V2v</font> = <font color="Maroon" title="c12">CSlv</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> ;<br/>
<a NAME="E11:138"/>
<font color="Maroon" title="c12">CSlv</font> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</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="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></i>;<br/>
<a NAME="E12:138"/><b>then </b><i><font color="Green" title="E109">A8</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">CSlv</font> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="lexbfs.html#E2"><i><font color="Green" title="E2">Tw0</font></i></a></i>;<br/>
<a NAME="E13:138"/><i><font color="Green" title="E110">A9</font></i>: 
<font color="Maroon" title="c12">CSlv</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a>  <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> 
 
<b>by </b><i><a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/>
<a NAME="E14:138"/><i><font color="Green" title="E111">A10</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">CSlv</font> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="#E12:138"><i><font color="Green" title="E109">A8</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E15:138"/><i><font color="Green" title="E112">A11</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<div><i><font color="Green" title="E113">A12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="138_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c15">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; not <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c15">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c15">v</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )</span><br/><b>assume </b><a NAME="E1:138_2"/><i><font color="Green" title="E114">A13</font></i>: 
( <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; not <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c15">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c15">v</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span><br/><a NAME="E2:138_2"/>
not <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="#E1:138_2"><i><font color="Green" title="E114">A13</font></i></a>, <a class="ref" href="chord.html#T49" title="CHORD:th.49">CHORD:49</a></i>;<br/><a NAME="E3:138_2"/><b>then </b>
not <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">CSlv</font> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span>
 <b>by </b><i><a class="txt" href="#E12:138"><i><font color="Green" title="E109">A8</font></i></a>, <a class="txt" href="#E1:138_2"><i><font color="Green" title="E114">A13</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E4:138_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c15">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c15">v</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="#E10:138"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="#E13:138"><i><font color="Green" title="E110">A9</font></i></a>, <a class="txt" href="#E1:138_2"><i><font color="Green" title="E114">A13</font></i></a>, <a class="ref" href="lexbfs.html#T62" target="_self" title="LEXBFS:th.62">Th76</a>, <a class="txt" href="#E15:138"><i><font color="Green" title="E112">A11</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E114">A16</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="138_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c15">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  not <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> or <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> ) implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><b>assume </b><a NAME="E1:138_3"/><i><font color="Green" title="E115">A17</font></i>: 
(  not <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> or <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="138_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:138_3_1"/>
(  not <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> or <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> )
 </span><b>by </b><i><a class="txt" href="#E1:138_3"><i><font color="Green" title="E115">A17</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="138_3_1_1"><b>suppose </b></a><a NAME="E1:138_3_1_1"/>
not <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><b>hence </b><a NAME="E2:138_3_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c15">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c15">v</font>
 <b>by </b><i><a class="txt" href="#E10:138"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="#E13:138"><i><font color="Green" title="E110">A9</font></i></a>, <a class="ref" href="lexbfs.html#T60" target="_self" title="LEXBFS:th.60">Th74</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="138_3_1_2"><b>suppose </b></a><a NAME="E1:138_3_1_2"/>
<font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><b>hence </b><a NAME="E2:138_3_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c15">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c15">v</font>
 <b>by </b><i><a class="txt" href="#E10:138"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="#E13:138"><i><font color="Green" title="E110">A9</font></i></a>, <a class="txt" href="#E14:138"><i><font color="Green" title="E111">A10</font></i></a>, <a class="ref" href="lexbfs.html#T61" target="_self" title="LEXBFS:th.61">Th75</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>take </b>
 <a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> &amp; ( for <font color="Olive" title="b1">v</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( ( <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; not <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">v</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 ) &amp; ( (  not <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> or <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> ) implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">v</font> ) ) ) )</span><br/>

<b>thus </b><a NAME="E18:138"/>
(  <a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> &amp; ( for <font color="Olive" title="b1">v</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( ( <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; not <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">v</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 ) &amp; ( (  not <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K19" title="LEXBFS:func.19">MCS:PickUnnumbered</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> or <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> </span>)</span> ) implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="lexbfs.html#K23" title="LEXBFS:func.23">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a> </span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">v</font> ) ) ) )
 <b>by </b><i><a class="txt" href="#E16:138"><i><font color="Green" title="E113">A12</font></i></a>, <a class="txt" href="#E17:138"><i><font color="Green" title="E114">A16</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
