<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E69">Th51</font></span>: <a NAME="T51"><span class="comment"><font color="firebrick">:: LEXBFS:51</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <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/>  for <font color="Olive" title="b2">i</font>, <font color="Olive" title="b3">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b1">G</font>  st <font color="Olive" title="b4">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="lexbfs.html#K13" title="LEXBFS:func.13">.</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> &amp; <font color="Olive" title="b5">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="lexbfs.html#K13" title="LEXBFS:func.13">.</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="lexbfs.html#K13" title="LEXBFS:func.13">.</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b4">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="lexbfs.html#K13" title="LEXBFS:func.13">.</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b5">b</font> &amp; <font color="Olive" title="b3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lexbfs.html#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="lexbfs.html#K13" title="LEXBFS:func.13">.</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b5">b</font></span>)</span> holds <br/>(<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#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="lexbfs.html#K13" title="LEXBFS:func.13">.</a> <font color="Olive" title="b3">j</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a></span>)</span> <a href="lexbfs.html#K17" title="LEXBFS:func.17">.</a> <font color="Olive" title="b4">a</font></span>)</span>,1) <a href="uproots.html#K1" title="UPROOTS:func.1">-bag</a>  <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</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#K16" title="LEXBFS:func.16">LexBFS:CSeq</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="lexbfs.html#K13" title="LEXBFS:func.13">.</a> <font color="Olive" title="b3">j</font></span>)</span> <a href="lexbfs.html#K8" title="LEXBFS:func.8">`2</a></span>)</span> <a href="lexbfs.html#K17" title="LEXBFS:func.17">.</a> <font color="Olive" title="b5">b</font></span>)</span>,1) <a href="uproots.html#K1" title="UPROOTS:func.1">-bag</a> , <a href="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></div></div>
