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<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_005.html#V1" title="GLIB_005:attr.1">natural-weighted</a>  <a href="glib_003.html#NM1" title="GLIB_003:NM.1">WGraph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K14" title="GLIB_005:func.14">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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K14" title="GLIB_005:func.14">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/>



<span class="kw">set </span><font color="Maroon" title="c4">CS</font> =  <a href="glib_005.html#K13" title="GLIB_005:func.13">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/>
<span class="kw">set </span><font color="Maroon" title="c5">n</font> = <span class="p1">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">Gn</font> = <span class="p1">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">Gn1</font> = <span class="p1">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<a NAME="E1:50"/><span class="lab"><font color="Green" title="E41">A1</font></span>: 
<span class="p1">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="glib_005.html#K11" title="GLIB_005:func.11">FF:Step</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_005.html#D20" target="_self" title="GLIB_005:def.20">Def20</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:50"/><span class="lab"><font color="Green" title="E42">A2</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="glib_005.html#K14" title="GLIB_005:func.14">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/>

<a NAME="E3:50"/><span class="kw">then </span>
 <a href="glib_005.html#K13" title="GLIB_005:func.13">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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_005.html#T17" target="_self" title="GLIB_005:th.17">Th17</a></span>;<br/>
<a NAME="E4:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A3</font></span>: 
<span class="p1">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D57" title="GLIB_000:def.57">GLIB_000:def 57</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><span class="kw">now </span></a><div class="add"><span class="kw">given </span><font color="Maroon" title="c8">P</font> being   <a href="glib_001.html#NM5" title="GLIB_001:NM.5">Path</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><a NAME="E2:50_1"/><span class="lab"><font color="Green" title="E44">A4</font></span>: 
<font color="Maroon" title="c8">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>
 <span class="kw">and </span><br/><a NAME="E3:50_1"/><span class="lab"><font color="Green" title="E45">A5</font></span>: 
<font color="Maroon" title="c8">P</font> <a href="glib_005.html#R5" title="GLIB_005:pred.5">is_augmenting_wrt</a> <span class="p1">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">set </span><font color="Maroon" title="c9">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#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font>;<br/><a NAME="E4:50_1"/><span class="lab"><font color="Green" title="E46">A6</font></span>: 
<font color="Maroon" title="c3">sink</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</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#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c2">source</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50_1"><span class="lab"><font color="Green" title="E44">A4</font></span></a>, <a class="txt" href="#E3:50_1"><span class="lab"><font color="Green" title="E45">A5</font></span></a>, <a class="ref" href="glib_005.html#T9" target="_self" title="GLIB_005:th.9">Th9</a></span>;<br/><a NAME="E5:50_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A7</font></span>: 
 <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#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_005.html#D14" target="_self" title="GLIB_005:def.14">Def14</a></span>;<br/><a NAME="E6:50_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A8</font></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#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">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="c2">source</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></span>;<br/><a NAME="E7:50_1"/><span class="lab"><font color="Green" title="E49">A9</font></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#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">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="c3">sink</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:50_1"><span class="lab"><font color="Green" title="E47">A7</font></span></a>, <a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></span>;<br/><a NAME="E8:50_1"/><span class="lab"><font color="Green" title="E50">A10</font></span>: 
 <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#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font> <a href="glib_005.html#R5" title="GLIB_005:pred.5">is_augmenting_wrt</a> <span class="p1">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:50_1"><span class="lab"><font color="Green" title="E46">A6</font></span></a>, <a class="ref" href="glib_005.html#D14" target="_self" title="GLIB_005:def.14">Def14</a></span>;<br/><a NAME="E9:50_1"/>
<span class="p1">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="glib_005.html#K10" title="GLIB_005:func.10">FF:PushFlow</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.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#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E41">A1</font></span></a>, <a class="txt" href="#E4:50_1"><span class="lab"><font color="Green" title="E46">A6</font></span></a>, <a class="ref" href="glib_005.html#D18" target="_self" title="GLIB_005:def.18">Def18</a></span>;<br/><a NAME="E10:50_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span></span>)</span> <a href="glib_005.html#K1" title="GLIB_005:func.1">.flow</a> <font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span></span>)</span>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span> <a href="glib_005.html#K9" title="GLIB_005:func.9">.tolerance</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.Lifespan()</a> </span>)</span></span>)</span></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#K13" title="GLIB_005:func.13">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#K12" title="GLIB_005:func.12">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K13" title="GLIB_005:func.13">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#K39" title="GLIB_000:func.39">.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#K1" title="GLIB_005:func.1">.flow</a> <font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E42">A2</font></span></a>, <a class="txt" href="#E5:50_1"><span class="lab"><font color="Green" title="E47">A7</font></span></a>, <a class="txt" href="#E8:50_1"><span class="lab"><font color="Green" title="E50">A10</font></span></a>, <a class="ref" href="glib_005.html#T15" target="_self" title="GLIB_005:th.15">Th15</a></span>;<br/><span class="kw">hence </span><a NAME="E11:50_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E42">A2</font></span></a>, <a class="txt" href="#E4:50"><span class="lab"><font color="Green" title="E43">A3</font></span></a>, <a class="txt" href="#E6:50_1"><span class="lab"><font color="Green" title="E48">A8</font></span></a>, <a class="txt" href="#E7:50_1"><span class="lab"><font color="Green" title="E49">A9</font></span></a>, <a class="txt" href="#E8:50_1"><span class="lab"><font color="Green" title="E50">A10</font></span></a>, <a class="ref" href="glib_005.html#T13" target="_self" title="GLIB_005:th.13">Th13</a>, <a class="ref" href="glib_001.html#T128" title="GLIB_001:th.128">GLIB_001:128</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:50"/>
 <a href="glib_005.html#K14" title="GLIB_005:func.14">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E42">A2</font></span></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></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
