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

<b>set </b><font color="Maroon" title="c4">P</font> =  <a href="glib_005.html#K7" title="GLIB_005:func.7">AP:GetAugPath</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:63_1_1_1_1"/>
( <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> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  or  not <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> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:63_1_1_1_1_1"/>
<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> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 ;<br/><div class="add"><a NAME="E2:63_1_1_1_1_1"/><b>then </b>
 <a href="glib_005.html#K13" title="GLIB_005:func.13">FF:Step</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_005.html#K12" title="GLIB_005:func.12">FF:AugmentPath</a> <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><a href="glib_005.html#K7" title="GLIB_005:func.7">AP:GetAugPath</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font>,<font color="Maroon" title="c3">sink</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D22" target="_self" title="GLIB_005:def.22">Def22</a></i>;<br/><b>hence </b><a NAME="E3:63_1_1_1_1_1"/>
 <a href="glib_005.html#K13" title="GLIB_005:func.13">FF:Step</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_003.html#V8" title="GLIB_003:attr.8">nonnegative-weighted</a>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:63_1_1_1_1_2"/>
not <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> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">source</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:63_1_1_1_1_2"/>
 <a href="glib_005.html#K13" title="GLIB_005:func.13">FF:Step</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_003.html#V8" title="GLIB_003:attr.8">nonnegative-weighted</a>
 <b>by </b><i><a class="ref" href="glib_005.html#D22" target="_self" title="GLIB_005:def.22">Def22</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:63_1_1"/>
 <a href="glib_005.html#K13" title="GLIB_005:func.13">FF:Step</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_003.html#V8" title="GLIB_003:attr.8">nonnegative-weighted</a>
 ;<br/>


</div>
