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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_005.html#V3" title="GLIB_005:attr.3">natural-weighted</a> <a href="glib_003.html#NM1" title="GLIB_003:NM.1">WGraph</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">source</font>, <font color="Olive" title="b2">sink</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b2">sink</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">source</font> holds <br/> <a href="glib_005.html#K16" title="GLIB_005:func.16">FF:MaxFlow</a> <font color="Maroon" title="c1">G</font>,<font color="Olive" title="b1">source</font>,<font color="Olive" title="b2">sink</font> <a href="glib_005.html#R2" title="GLIB_005:pred.2">has_maximum_flow_from</a> <font color="Olive" title="b1">source</font>,<font color="Olive" title="b2">sink</font></span><br/><b>let </b><font color="Maroon" title="c2">source</font>, <font color="Maroon" title="c3">sink</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">sink</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">source</font> implies  <a href="glib_005.html#K16" title="GLIB_005:func.16">FF:MaxFlow</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font> <a href="glib_005.html#R2" title="GLIB_005:pred.2">has_maximum_flow_from</a> <font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font> )</span><br/>



<b>set </b><font color="Maroon" title="c4">CS</font> =  <a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font>;<br/>
<b>assume </b><a NAME="E1:82"/><i><font color="Green" title="E40">A1</font></i>: 
<font color="Maroon" title="c3">sink</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">source</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="glib_005.html#K16" title="GLIB_005:func.16">FF:MaxFlow</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font> <a href="glib_005.html#R2" title="GLIB_005:pred.2">has_maximum_flow_from</a> <font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span><br/>

<b>set </b><font color="Maroon" title="c5">n</font> = <span class="p1">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> ;<br/>
<b>set </b><font color="Maroon" title="c6">Gn</font> = <span class="p1">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c7">Gn1</font> = <span class="p1">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c8">source'</font>, <font color="Maroon" title="c9">sink'</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:82"/><i><font color="Green" title="E41">A2</font></i>: 
( <font color="Maroon" title="c8">source'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">source</font> &amp; <font color="Maroon" title="c9">sink'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">sink</font> &amp; <span class="p1">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_005.html#K13" title="GLIB_005:func.13">FF:Step</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c8">source'</font>,<font color="Maroon" title="c9">sink'</font> )
 <b>by </b><i><a class="ref" href="glib_005.html#D23" target="_self" title="GLIB_005:def.23">Def23</a></i>;<br/>
<a NAME="E4:82"/>
 <a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font> is <a href="glib_000.html#V13" title="GLIB_000:attr.13">halting</a>
 
<b>by </b><i><a class="txt" href="glib_005.html#E1:82"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="glib_005.html#T19" target="_self" title="GLIB_005:th.19">Th19</a></i>;<br/>
<a NAME="E5:82"/><b>then </b><i><font color="Green" title="E42">A3</font></i>: 
<span class="p1">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="glib_000.html#D57" title="GLIB_000:def.57">GLIB_000:def 57</a></i>;<br/>
<a NAME="E6:82"/><i><font color="Green" title="E43">A4</font></i>: 
<span class="p1">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="glib_005.html#R1" title="GLIB_005:pred.1">has_valid_flow_from</a> <font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font>
 
<b>by </b><i><a class="txt" href="glib_005.html#E1:82"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="glib_005.html#T18" target="_self" title="GLIB_005:th.18">Th18</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon" title="c10">P</font> being  <a href="glib_005.html#V7" title="GLIB_005:attr.7">augmenting</a> <a href="glib_001.html#NM5" title="GLIB_001:NM.5">Path</a> of <span class="p1">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span><b> such that </b><a NAME="E2:82_1"/><i><font color="Green" title="E44">A5</font></i>: 
<font color="Maroon" title="c10">P</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E3:82_1"/><i><font color="Green" title="E45">A6</font></i>: 
<font color="Maroon" title="c3">sink</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="glib_005.html#K6" title="GLIB_005:func.6">AP:FindAugPath</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c8">source'</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 <b>by </b><i><a class="txt" href="glib_005.html#E3:82"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="glib_005.html#E2:82_1"><i><font color="Green" title="E44">A5</font></i></a>, <a class="ref" href="glib_005.html#T9" target="_self" title="GLIB_005:th.9">Th9</a></i>;<br/><a NAME="E4:82_1"/><b>then </b><i><font color="Green" title="E46">A7</font></i>: 
<span class="p1">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_005.html#K12" title="GLIB_005:func.12">FF:AugmentPath</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="glib_005.html#K7" title="GLIB_005:func.7">AP:GetAugPath</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c8">source'</font>,<font color="Maroon" title="c9">sink'</font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E3:82"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="glib_005.html#D22" target="_self" title="GLIB_005:def.22">Def22</a></i>;<br/><b>set </b><font color="Maroon" title="c11">P</font> =  <a href="glib_005.html#K7" title="GLIB_005:func.7">AP:GetAugPath</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c8">source'</font>,<font color="Maroon" title="c9">sink'</font>;<br/><a NAME="E5:82_1"/><i><font color="Green" title="E47">A8</font></i>: 
 <a href="glib_005.html#K7" title="GLIB_005:func.7">AP:GetAugPath</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c8">source'</font>,<font color="Maroon" title="c9">sink'</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c8">source'</font>,<font color="Maroon" title="c9">sink'</font>
 <b>by </b><i><a class="txt" href="glib_005.html#E3:82"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="glib_005.html#E3:82_1"><i><font color="Green" title="E45">A6</font></i></a>, <a class="ref" href="glib_005.html#D17" target="_self" title="GLIB_005:def.17">Def17</a></i>;<br/><a NAME="E6:82_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="glib_005.html#K7" title="GLIB_005:func.7">AP:GetAugPath</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c8">source'</font>,<font color="Maroon" title="c9">sink'</font></span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">source'</font> &amp; <span class="p1">(<span class="default"><a href="glib_005.html#K7" title="GLIB_005:func.7">AP:GetAugPath</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c8">source'</font>,<font color="Maroon" title="c9">sink'</font></span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">sink'</font> )
 <b>by </b><i><a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></i>;<br/><a NAME="E7:82_1"/><b>then </b><i><font color="Green" title="E48">A9</font></i>: 
not  <a href="glib_005.html#K7" title="GLIB_005:func.7">AP:GetAugPath</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c8">source'</font>,<font color="Maroon" title="c9">sink'</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:82"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="glib_005.html#E3:82"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="glib_001.html#T128" title="GLIB_001:th.128">GLIB_001:128</a></i>;<br/><a NAME="E8:82_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span> <a href="glib_005.html#K2" title="GLIB_005:func.2">.flow</a> <font color="Maroon" title="c8">source'</font>,<font color="Maroon" title="c9">sink'</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K7" title="GLIB_005:func.7">AP:GetAugPath</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c8">source'</font>,<font color="Maroon" title="c9">sink'</font></span>)</span> <a href="glib_005.html#K10" title="GLIB_005:func.10">.tolerance()</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K14" title="GLIB_005:func.14">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K15" title="GLIB_005:func.15">FF:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="glib_005.html#K2" title="GLIB_005:func.2">.flow</a> <font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:82"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="glib_005.html#E3:82"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="glib_005.html#E4:82_1"><i><font color="Green" title="E46">A7</font></i></a>, <a class="txt" href="glib_005.html#E5:82_1"><i><font color="Green" title="E47">A8</font></i></a>, <a class="ref" href="glib_005.html#T16" target="_self" title="GLIB_005:th.16">Th16</a>, <a class="ref" href="glib_005.html#T18" target="_self" title="GLIB_005:th.18">Th18</a></i>;<br/><b>hence </b><a NAME="E9:82_1"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_005.html#E3:82"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="glib_005.html#E5:82"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="glib_005.html#E7:82_1"><i><font color="Green" title="E48">A9</font></i></a>, <a class="ref" href="glib_005.html#T14" target="_self" title="GLIB_005:th.14">Th14</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>
<b>hence </b><a NAME="E8:82"/>
 <a href="glib_005.html#K16" title="GLIB_005:func.16">FF:MaxFlow</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font> <a href="glib_005.html#R2" title="GLIB_005:pred.2">has_maximum_flow_from</a> <font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:82"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="glib_005.html#E6:82"><i><font color="Green" title="E43">A4</font></i></a>, <a class="ref" href="glib_005.html#T20" target="_self" title="GLIB_005:th.20">Th20</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>
