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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="glib_000.html#V2">finite</a> <a href="glib_005.html#V3" target="_self">natural-weighted</a> <a href="glib_003.html#NM1">WGraph</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<b>assume </b><a NAME="E1:77"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being   <a href="glib_000.html#NM10">Vertex</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:77"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="glib_005.html#K13" target="_self">FF:Step</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="ref" href="glib_005.html#D23" target="_self">Def23</a></i>;<br/>
<a NAME="E4:77"/>
 <a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> is <a href="glib_000.html#V13">halting</a>
 
<b>by </b><i><a class="txt" href="glib_005.html#E1:77"><i><font color="Green">E41</font></i></a>, <a class="ref" href="glib_005.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E5:77"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="glib_000.html#D57">GLIB_000:def 57</a></i>;<br/>
<a NAME="E6:77"/><b>then </b><i><font color="Green">E43</font></i>: 
<span class="p1">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
;<br/>
<a NAME="E7:77"/><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span> <a href="glib_005.html#R1" target="_self">has_valid_flow_from</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="glib_005.html#E1:77"><i><font color="Green">E41</font></i></a>, <a class="ref" href="glib_005.html#T18" target="_self">Th18</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">c<sub>10</sub></font> being  <a href="glib_005.html#V7" target="_self">augmenting</a> <a href="glib_001.html#NM5">Path</a> of <span class="p1">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span><b> such that </b><a NAME="E1:77_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:77_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_005.html#K6" target="_self">AP:FindAugPath</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> 
 <b>by </b><i><a class="txt" href="glib_005.html#E3:77"><i><font color="Green">E42</font></i></a>, <a class="txt" href="glib_005.html#E1:77_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="glib_005.html#T9" target="_self">Th9</a></i>;<br/><a NAME="E3:77_1"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="glib_005.html#K7" target="_self">AP:GetAugPath</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E3:77"><i><font color="Green">E42</font></i></a>, <a class="ref" href="glib_005.html#D22" target="_self">Def22</a></i>;<br/><b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="glib_005.html#K7" target="_self">AP:GetAugPath</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/><a NAME="E4:77_1"/><i><font color="Green">E48</font></i>: 
 <a href="glib_005.html#K7" target="_self">AP:GetAugPath</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E3:77"><i><font color="Green">E42</font></i></a>, <a class="txt" href="glib_005.html#E2:77_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="glib_005.html#D17" target="_self">Def17</a></i>;<br/><a NAME="E5:77_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="glib_005.html#K7" target="_self">AP:GetAugPath</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="glib_001.html#K3">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_005.html#K7" target="_self">AP:GetAugPath</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="glib_001.html#K4">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="ref" href="glib_001.html#D23">GLIB_001:def 23</a></i>;<br/><a NAME="E6:77_1"/><b>then </b>
not  <a href="glib_005.html#K7" target="_self">AP:GetAugPath</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> is <a href="glib_001.html#V3">trivial</a>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:77"><i><font color="Green">E41</font></i></a>, <a class="txt" href="glib_005.html#E3:77"><i><font color="Green">E42</font></i></a>, <a class="ref" href="glib_001.html#T128">GLIB_001:128</a></i>;<br/><a NAME="E7:77_1"/><b>then </b><i><font color="Green">E49</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="glib_005.html#K7" target="_self">AP:GetAugPath</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="glib_005.html#K10" target="_self">.tolerance()</a> 
 <b>by </b><i><a class="ref" href="glib_005.html#T14" target="_self">Th14</a></i>;<br/><a NAME="E8:77_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span> <a href="glib_005.html#K2" target="_self">.flow</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K7" target="_self">AP:GetAugPath</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="glib_005.html#K10" target="_self">.tolerance()</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="glib_005.html#K2" target="_self">.flow</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:77"><i><font color="Green">E41</font></i></a>, <a class="txt" href="glib_005.html#E3:77"><i><font color="Green">E42</font></i></a>, <a class="txt" href="glib_005.html#E7:77"><i><font color="Green">E44</font></i></a>, <a class="txt" href="glib_005.html#E3:77_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="glib_005.html#E4:77_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="glib_005.html#T16" target="_self">Th16</a></i>;<br/><a NAME="E9:77_1"/><b>then </b>
<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="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span> <a href="glib_005.html#K2" target="_self">.flow</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K7" target="_self">AP:GetAugPath</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="glib_005.html#K10" target="_self">.tolerance()</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K7" target="_self">AP:GetAugPath</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="glib_005.html#K10" target="_self">.tolerance()</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K14" target="_self">FF:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="glib_005.html#K2" target="_self">.flow</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 0
 <b>by </b><i><a class="txt" href="glib_005.html#E7:77_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><b>hence </b><a NAME="E10:77_1"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_005.html#E3:77"><i><font color="Green">E42</font></i></a>, <a class="txt" href="glib_005.html#E6:77"><i><font color="Green">E43</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:77"/>
 <a href="glib_005.html#K15" target="_self">FF:MaxFlow</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="glib_005.html#R2" target="_self">has_maximum_flow_from</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:77"><i><font color="Green">E41</font></i></a>, <a class="txt" href="glib_005.html#E7:77"><i><font color="Green">E44</font></i></a>, <a class="ref" href="glib_005.html#T20" target="_self">Th20</a></i>;<br/>


</div>
