<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#V2" title="GLIB_000:attr.2">_finite</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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="glib_000.html#K39" title="GLIB_000:func.39">.Lifespan()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">CS</font> =  <a href="lexbfs.html#K26" title="LEXBFS:func.26">MCS:CSeq</a> <font color="Maroon" title="c1">G</font>;<br/>
<a NAME="E1:126"/><span class="lab"><font color="Green" title="E92">A1</font></span>: 
 for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <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="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> holds <br/><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="126_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> implies <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">n</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:126_1"/><span class="lab"><font color="Green" title="E93">A2</font></span>: 
<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="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">n</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">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="c3">n</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">VN1</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="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">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="c3">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">j</font> =  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">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="c3">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">wf</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="c3">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p3">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p4">(<span class="default"><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="c3">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<span class="kw">assume </span><a NAME="E2:126_1"/><span class="lab"><font color="Green" title="E94">A3</font></span>: 
<font color="Maroon" title="c3">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#K15" title="GLIB_000:func.15">.order()</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:126_1"/><span class="kw">then </span>
 <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#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="c3">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lexbfs.html#T69" target="_self" onmouseover="rs('lexbfs/T69')" onmouseout="rh()">Th69</a></span>;<br/>
<a NAME="E4:126_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E95">A4</font></span>: 
 not  <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="c3">n</font></span>)</span> <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#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="c3">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lexbfs.html#T59" target="_self" onmouseover="rs('lexbfs/T59')" onmouseout="rh()">Th59</a></span>;<br/>
<a NAME="E5:126_1"/>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">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="c3">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:126_1"><span class="lab"><font color="Green" title="E94">A3</font></span></a>, <a class="ref" href="lexbfs.html#T65" target="_self" onmouseover="rs('lexbfs/T65')" onmouseout="rh()">Th65</a></span>;<br/>
<a NAME="E6:126_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A5</font></span>: 
<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="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <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="c3">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="c3">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&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#K15" title="GLIB_000:func.15">.order()</a></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p4">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><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="c3">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lexbfs.html#T64" target="_self" onmouseover="rs('lexbfs/T64')" onmouseout="rh()">Th64</a></span>;<br/>
<a NAME="E7:126_1"/>
 <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"><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="c3">n</font></span>)</span></span>)</span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&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#K15" title="GLIB_000:func.15">.order()</a></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p4">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><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="c3">n</font></span>)</span> <a href="lexbfs.html#K7" title="LEXBFS:func.7">`1</a></span>)</span></span>)</span></span>)</span></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"><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="c3">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
;<br/>
<a NAME="E8:126_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E97">A6</font></span>: 
 <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#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="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <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#K1" title="RELSET_1:func.1">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="c3">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="c3">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:126_1"><span class="lab"><font color="Green" title="E96">A5</font></span></a>, <a class="ref" href="funct_4.html#D1" onmouseover="rs('funct_4/D1')" onmouseout="rh()">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E9:126_1"/>
 <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="c3">n</font></span>)</span> <a href="tarski.html#R2" title="TARSKI: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="c3">n</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:126_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126_1"><span class="lab"><font color="Green" title="E93">A2</font></span></a>, <a class="txt" href="#E4:126_1"><span class="lab"><font color="Green" title="E95">A4</font></span></a>, <a class="txt" href="#E8:126_1"><span class="lab"><font color="Green" title="E97">A6</font></span></a>, <a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:126"/>
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E3:126"/><span class="kw">then </span>
<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="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lexbfs.html#T66" target="_self" onmouseover="rs('lexbfs/T66')" onmouseout="rh()">Th66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:126"/>
<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="glib_000.html#K39" title="GLIB_000:func.39">.Lifespan()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126"><span class="lab"><font color="Green" title="E92">A1</font></span></a>, <a class="ref" href="glib_000.html#D56" onmouseover="rs('glib_000/D56')" onmouseout="rh()">GLIB_000:def 56</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
