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<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_003.html#V7">real-weighted</a> <a href="glib_003.html#V9">real-elabeled</a> <a href="glib_005.html#V1" target="_self">complete-elabeled</a> <a href="glib_003.html#NM4">WEGraph</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="glib_005.html#V7" target="_self">augmenting</a> <a href="glib_001.html#NM5">Path</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:71"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <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> &amp; <font color="Maroon">c<sub>4</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/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<i><font color="Green">E38</font></i>:  <a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_003.html#K3">ELabelSelector</a> 

<br/>.= 
 <a href="glib_005.html#K11" target="_self">FF:PushFlow</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="glib_000.html#T11">GLIB_000:11</a></i>
;<br/>
<a NAME="E3:71"/><i><font color="Green">E39</font></i>: 
 <a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> <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#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_005.html#T15" target="_self">Th15</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> = <span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span>;<br/>
<a NAME="E4:71"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="glib_001.html#K3">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="glib_001.html#K4">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_001.html#D23">GLIB_001:def 23</a></i>;<br/>
<a NAME="E5:71"/><b>then </b>
not <font color="Maroon">c<sub>4</sub></font> is <a href="glib_001.html#V3">trivial</a>
 
<b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_001.html#T128">GLIB_001:128</a></i>;<br/>
<a NAME="E6:71"/><b>then </b>
3 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="glib_001.html#T126">GLIB_001:126</a></i>;<br/>
<a NAME="E7:71"/><b>then </b>
2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> as  <a href="abian.html#V1">odd</a> <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="ref" href="int_1.html#T18">INT_1:18</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<a NAME="E9:71"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 0
 
<b>by </b><i><a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/>
<a NAME="E10:71"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="glib_001.html#D3">GLIB_001:def 3</a></i>;<br/>
<a NAME="E11:71"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="glib_000.html#D15">GLIB_000:def 15</a></i>;<br/>
<a NAME="E12:71"/>
 <a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="glib_000.html#R5">==</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="glib_005.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E13:71"/><b>then </b><i><font color="Green">E43</font></i>: 
( <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="glib_000.html#T93">GLIB_000:93</a></i>;<br/>
<a NAME="E14:71"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:71_2_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="glib_000.html#R2">DJoins</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font> or  not <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="glib_000.html#R2">DJoins</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_1"><b>suppose </b></a><a NAME="E1:71_2_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="glib_000.html#R2">DJoins</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:71_2_1_1"/><b>then </b><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p2">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></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#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E2:71"><i><font color="Green">E38</font></i></a>, <a class="txt" href="glib_005.html#E9:71"><i><font color="Green">E40</font></i></a>, <a class="ref" href="glib_005.html#D20" target="_self">Def20</a></i>;<br/><span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="glib_005.html#E1:71_2_1_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="glib_000.html#D16">GLIB_000:def 16</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a></i>
;<br/><a NAME="E4:71_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E5:71_2_1_1"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="glib_005.html#E11:71"><i><font color="Green">E42</font></i></a>, <a class="ref" href="glib_000.html#D28">GLIB_000:def 28</a></i>;<br/><b>set </b><font color="Maroon">c<sub>13</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span>;<br/><i><font color="Green">E48</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="txt" href="glib_005.html#E5:71_2_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
;<br/><b>then reconsider </b><font color="Maroon">c<sub>14</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span> as   <a href="uproots.html#NM1">Rbag</a> of <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span> <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E8:71_2_1_1"/><i><font color="Green">E49</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:71_2_1_1_3"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:71_2_1_1_3"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E3:71_2_1_1_3"/><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p2">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71_2_1_1_3"><i><font color="Green">E50</font></i></a>, <a class="txt" href="glib_005.html#E8:71_2_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E4:71_2_1_1_3"/>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="glib_005.html#E2:71_2_1_1_3"><i><font color="Green">E51</font></i></a>, <a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="ref" href="glib_000.html#D28">GLIB_000:def 28</a></i>;<br/><a NAME="E5:71_2_1_1_3"/><b>then </b><i><font color="Green">E53</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_1_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:71_2_1_1_3_1_1"/>
( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> or <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:71_2_1_1_3_1_1_1"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><div class="add"><a NAME="E2:71_2_1_1_3_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:71_2_1_1_3_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><b>then </b><font color="Maroon">c<sub>14</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="glib_005.html#E1:71_2_1_1_3_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p2">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="glib_005.html#E2:71_2_1_1_3"><i><font color="Green">E51</font></i></a>, <a class="txt" href="glib_005.html#E2:71_2_1_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="txt" href="glib_005.html#E1:71_2_1_1_3_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E5:71_2_1_1_3_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71_2_1_1_3"><i><font color="Green">E50</font></i></a>, <a class="txt" href="glib_005.html#E8:71_2_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a>, <a class="txt" href="glib_005.html#E1:71_2_1_1_3_1_1_1"><i><font color="Green">E54</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:71_2_1_1_3_1_1_2"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><div class="add"><a NAME="E2:71_2_1_1_3_1_1_2"/><b>then </b>
not <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:71_2_1_1_3_1_1_2"/><b>then </b>
not <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><b>then </b><i><font color="Green">E55</font></i>: <font color="Maroon">c<sub>14</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="glib_005.html#E2:71_2_1_1_3"><i><font color="Green">E51</font></i></a>, <a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_1_3_1_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:71_2_1_1_3_1_1_2_2"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="glib_001.html#K14">.edges()</a> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>17</sub></font> being   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>18</sub></font> being  <a href="abian.html#V1">odd</a> <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:71_2_1_1_3_1_1_2_2"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="glib_001.html#T104">GLIB_001:104</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_1_3_1_1_2_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_1_3_1_1_2_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:71_2_1_1_3_1_1_2_2_1_1"/>
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 </span><b>by </b><i><a class="txt" href="glib_005.html#E3:71_2_1_1_3_1_1_2_2"><i><font color="Green">E56</font></i></a>, <a class="txt" href="glib_005.html#E5:71_2_1_1_3"><i><font color="Green">E53</font></i></a>, <a class="ref" href="glib_000.html#D15">GLIB_000:def 15</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_1_3_1_1_2_2_1_1_1"><b>suppose </b></a><a NAME="E1:71_2_1_1_3_1_1_2_2_1_1_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:71_2_1_1_3_1_1_2_2_1_1_1"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a>, <a class="txt" href="glib_005.html#E3:71_2_1_1_3_1_1_2_2"><i><font color="Green">E56</font></i></a></i>;<br/><a NAME="E3:71_2_1_1_3_1_1_2_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="real_1.html#K5">-</a> 2 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 0
 <b>by </b><i><a class="txt" href="glib_005.html#E3:71_2_1_1_3_1_1_2_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E4:71_2_1_1_3_1_1_2_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_005.html#E2:71_2_1_1_3_1_1_2_2_1_1_1"><i><font color="Green">E58</font></i></a>, <a class="ref" href="glib_001.html#D28">GLIB_001:def 28</a></i>;<br/><b>hence </b><a NAME="E5:71_2_1_1_3_1_1_2_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="txt" href="glib_005.html#E1:71_2_1_1_3_1_1_2_2_1_1_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a>, <a class="txt" href="glib_005.html#E3:71_2_1_1_3_1_1_2_2"><i><font color="Green">E56</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_1_3_1_1_2_2_1_1_2"><b>suppose </b></a><a NAME="E1:71_2_1_1_3_1_1_2_2_1_1_2"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:71_2_1_1_3_1_1_2_2_1_1_2"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a>, <a class="txt" href="glib_005.html#E3:71_2_1_1_3_1_1_2_2"><i><font color="Green">E56</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_1_3_1_1_2_2_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:71_2_1_1_3_1_1_2_2_1_1_2_1"/>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:71_2_1_1_3_1_1_2_2_1_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_005.html#E2:71_2_1_1_3_1_1_2_2_1_1_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="glib_001.html#D28">GLIB_001:def 28</a></i>;<br/><a NAME="E3:71_2_1_1_3_1_1_2_2_1_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K5">-</a> 2
 ;<br/><b>hence </b><a NAME="E4:71_2_1_1_3_1_1_2_2_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="ref" href="heyting3.html#T1">HEYTING3:1</a></i>;<br/></div><b>end;</b></div><a NAME="E4:71_2_1_1_3_1_1_2_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E3:71_2_1_1_3_1_1_2_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><b>hence </b><a NAME="E5:71_2_1_1_3_1_1_2_2_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71_2_1_1_3_1_1_2"><i><font color="Green">E54</font></i></a>, <a class="txt" href="glib_005.html#E3:71_2_1_1_3_1_1_2_2"><i><font color="Green">E56</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:71_2_1_1_3_1_1_2_2"/>
contradiction
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:71_2_1_1_3_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E2:71_2_1_1_3"><i><font color="Green">E51</font></i></a>, <a class="txt" href="glib_005.html#E3:71_2_1_1_3"><i><font color="Green">E52</font></i></a>, <a class="txt" href="glib_005.html#E4:71_2_1_1_3_1_1_2"><i><font color="Green">E55</font></i></a>, <a class="txt" href="glib_005.html#E2:71"><i><font color="Green">E38</font></i></a>, <a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="ref" href="glib_005.html#D20" target="_self">Def20</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E7:71_2_1_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/></div><b>end;</b></div><b>then </b><i><font color="Green">E50</font></i>:  <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> = 
 <a href="uproots.html#K3">Sum</a> <font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="txt" href="glib_005.html#E6:71_2_1_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="glib_005.html#E8:71_2_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="glib_004.html#T9">GLIB_004:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span>

;<br/><a NAME="E11:71_2_1_1"/><i><font color="Green">E51</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_1_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:71_2_1_1_5"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:71_2_1_1_5"/><b>then </b><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E3:71_2_1_1_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="ref" href="glib_000.html#D29">GLIB_000:def 29</a></i>;<br/><a NAME="E4:71_2_1_1_5"/><b>then </b><i><font color="Green">E54</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_1_5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:71_2_1_1_5_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="glib_001.html#K14">.edges()</a> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>17</sub></font> being   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>18</sub></font> being  <a href="abian.html#V1">odd</a> <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:71_2_1_1_5_1"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="glib_001.html#T104">GLIB_001:104</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_1_5_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_1_5_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:71_2_1_1_5_1_1_1"/>
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 </span><b>by </b><i><a class="txt" href="glib_005.html#E4:71_2_1_1_5"><i><font color="Green">E54</font></i></a>, <a class="txt" href="glib_005.html#E3:71_2_1_1_5_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="glib_000.html#D15">GLIB_000:def 15</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_1_5_1_1_1_1"><b>suppose </b></a><a NAME="E1:71_2_1_1_5_1_1_1_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:71_2_1_1_5_1_1_1_1"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a>, <a class="txt" href="glib_005.html#E3:71_2_1_1_5_1"><i><font color="Green">E55</font></i></a></i>;<br/><a NAME="E3:71_2_1_1_5_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="real_1.html#K5">-</a> 2 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 0
 <b>by </b><i><a class="txt" href="glib_005.html#E3:71_2_1_1_5_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E4:71_2_1_1_5_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_005.html#E2:71_2_1_1_5_1_1_1_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="glib_001.html#D28">GLIB_001:def 28</a></i>;<br/><b>hence </b><a NAME="E5:71_2_1_1_5_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="txt" href="glib_005.html#E3:71_2_1_1_5_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="glib_005.html#E1:71_2_1_1_5_1_1_1_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_1_5_1_1_1_2"><b>suppose </b></a><a NAME="E1:71_2_1_1_5_1_1_1_2"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:71_2_1_1_5_1_1_1_2"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a>, <a class="txt" href="glib_005.html#E3:71_2_1_1_5_1"><i><font color="Green">E55</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_1_5_1_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:71_2_1_1_5_1_1_1_2_1"/>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:71_2_1_1_5_1_1_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_005.html#E2:71_2_1_1_5_1_1_1_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="glib_001.html#D28">GLIB_001:def 28</a></i>;<br/><a NAME="E3:71_2_1_1_5_1_1_1_2_1"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K5">-</a> 2
 <b>by </b><i><a class="ref" href="heyting3.html#T1">HEYTING3:1</a></i>;<br/><b>hence </b><a NAME="E4:71_2_1_1_5_1_1_1_2_1"/>
contradiction
 ;<br/></div><b>end;</b></div><a NAME="E4:71_2_1_1_5_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E3:71_2_1_1_5_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E5:71_2_1_1_5_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E6:71_2_1_1_5_1_1_1_2"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E3:71_2_1_1_5_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="glib_005.html#E1:71_2_1_1"><i><font color="Green">E45</font></i></a>, <a class="txt" href="glib_005.html#E4:71_2_1_1_5"><i><font color="Green">E54</font></i></a>, <a class="ref" href="glib_000.html#D16">GLIB_000:def 16</a></i>;<br/><a NAME="E7:71_2_1_1_5_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_005.html#E14:71"><i><font color="Green">E44</font></i></a>, <a class="txt" href="glib_005.html#E9:71"><i><font color="Green">E40</font></i></a>, <a class="ref" href="glib_001.html#D28">GLIB_001:def 28</a></i>;<br/><b>hence </b><a NAME="E8:71_2_1_1_5_1_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="txt" href="glib_005.html#E6:71_2_1_1_5_1_1_1_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:71_2_1_1_5_1"/>
contradiction
 ;<br/></div><b>end;</b></div><b>then </b><span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p2">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="glib_005.html#E2:71"><i><font color="Green">E38</font></i></a>, <a class="txt" href="glib_005.html#E2:71_2_1_1_5"><i><font color="Green">E53</font></i></a>, <a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="ref" href="glib_005.html#D20" target="_self">Def20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="txt" href="glib_005.html#E2:71_2_1_1_5"><i><font color="Green">E53</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E7:71_2_1_1_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a>, <a class="txt" href="glib_005.html#E1:71_2_1_1_5"><i><font color="Green">E52</font></i></a>, <a class="txt" href="glib_005.html#E11:71_2_1_1"><i><font color="Green">E51</font></i></a></i>;<br/></div><b>end;</b></div><a NAME="E13:71_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p2">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E11:71_2_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E14:71_2_1_1"/><b>then </b>
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_004.html#T7">GLIB_004:7</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></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 class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="glib_005.html#E10:71_2_1_1"><i><font color="Green">E50</font></i></a>, <a class="txt" href="glib_005.html#E3:71"><i><font color="Green">E39</font></i></a>, <a class="ref" href="glib_005.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <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#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span>
<b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_005.html#D8" target="_self">Def8</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_2"><b>suppose </b></a><a NAME="E1:71_2_1_2"/><i><font color="Green">E45</font></i>: 
not <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="glib_000.html#R2">DJoins</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:71_2_1_2"/><b>then </b><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p2">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></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#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E2:71"><i><font color="Green">E38</font></i></a>, <a class="txt" href="glib_005.html#E9:71"><i><font color="Green">E40</font></i></a>, <a class="ref" href="glib_005.html#D20" target="_self">Def20</a></i>;<br/><a NAME="E3:71_2_1_2"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="glib_000.html#R2">DJoins</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E10:71"><i><font color="Green">E41</font></i></a>, <a class="txt" href="glib_005.html#E1:71_2_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="glib_000.html#T19">GLIB_000:19</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="glib_000.html#D16">GLIB_000:def 16</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a></i>
;<br/><a NAME="E5:71_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E6:71_2_1_2"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="glib_005.html#E11:71"><i><font color="Green">E42</font></i></a>, <a class="ref" href="glib_000.html#D29">GLIB_000:def 29</a></i>;<br/><b>set </b><font color="Maroon">c<sub>13</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span>;<br/><i><font color="Green">E49</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="txt" href="glib_005.html#E6:71_2_1_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
;<br/><b>then reconsider </b><font color="Maroon">c<sub>14</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span> as   <a href="uproots.html#NM1">Rbag</a> of <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span> <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E9:71_2_1_2"/><i><font color="Green">E50</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_2_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:71_2_1_2_3"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:71_2_1_2_3"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E3:71_2_1_2_3"/><i><font color="Green">E53</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p2">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71_2_1_2_3"><i><font color="Green">E51</font></i></a>, <a class="txt" href="glib_005.html#E9:71_2_1_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E4:71_2_1_2_3"/>
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="txt" href="glib_005.html#E2:71_2_1_2_3"><i><font color="Green">E52</font></i></a>, <a class="ref" href="glib_000.html#D29">GLIB_000:def 29</a></i>;<br/><a NAME="E5:71_2_1_2_3"/><b>then </b><i><font color="Green">E54</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_2_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_2_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:71_2_1_2_3_1_1"/>
( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> or <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_2_3_1_1_1"><b>suppose </b></a><a NAME="E1:71_2_1_2_3_1_1_1"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><div class="add"><a NAME="E2:71_2_1_2_3_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:71_2_1_2_3_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><b>then </b><font color="Maroon">c<sub>14</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="glib_005.html#E1:71_2_1_2_3_1_1_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p2">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="glib_005.html#E2:71_2_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="txt" href="glib_005.html#E2:71_2_1_2_3"><i><font color="Green">E52</font></i></a>, <a class="txt" href="glib_005.html#E1:71_2_1_2_3_1_1_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E5:71_2_1_2_3_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71_2_1_2_3"><i><font color="Green">E51</font></i></a>, <a class="txt" href="glib_005.html#E9:71_2_1_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_2_3_1_1_2"><b>suppose </b></a><a NAME="E1:71_2_1_2_3_1_1_2"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><div class="add"><a NAME="E2:71_2_1_2_3_1_1_2"/><b>then </b>
not <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:71_2_1_2_3_1_1_2"/><b>then </b>
not <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><b>then </b><i><font color="Green">E56</font></i>: <font color="Maroon">c<sub>14</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="txt" href="glib_005.html#E2:71_2_1_2_3"><i><font color="Green">E52</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_2_3_1_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:71_2_1_2_3_1_1_2_2"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="glib_001.html#K14">.edges()</a> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>17</sub></font> being   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>18</sub></font> being  <a href="abian.html#V1">odd</a> <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:71_2_1_2_3_1_1_2_2"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="glib_001.html#T104">GLIB_001:104</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_2_3_1_1_2_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_2_3_1_1_2_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:71_2_1_2_3_1_1_2_2_1_1"/>
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 </span><b>by </b><i><a class="txt" href="glib_005.html#E5:71_2_1_2_3"><i><font color="Green">E54</font></i></a>, <a class="txt" href="glib_005.html#E3:71_2_1_2_3_1_1_2_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="glib_000.html#D15">GLIB_000:def 15</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_2_3_1_1_2_2_1_1_1"><b>suppose </b></a><a NAME="E1:71_2_1_2_3_1_1_2_2_1_1_1"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:71_2_1_2_3_1_1_2_2_1_1_1"/><b>then </b><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a>, <a class="txt" href="glib_005.html#E3:71_2_1_2_3_1_1_2_2"><i><font color="Green">E57</font></i></a></i>;<br/><a NAME="E3:71_2_1_2_3_1_1_2_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="real_1.html#K5">-</a> 2 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 0
 <b>by </b><i><a class="txt" href="glib_005.html#E3:71_2_1_2_3_1_1_2_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E4:71_2_1_2_3_1_1_2_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_005.html#E2:71_2_1_2_3_1_1_2_2_1_1_1"><i><font color="Green">E59</font></i></a>, <a class="ref" href="glib_001.html#D28">GLIB_001:def 28</a></i>;<br/><b>hence </b><a NAME="E5:71_2_1_2_3_1_1_2_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="txt" href="glib_005.html#E1:71_2_1_2_3_1_1_2_2_1_1_1"><i><font color="Green">E58</font></i></a>, <a class="txt" href="glib_005.html#E3:71_2_1_2_3_1_1_2_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_2_3_1_1_2_2_1_1_2"><b>suppose </b></a><a NAME="E1:71_2_1_2_3_1_1_2_2_1_1_2"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:71_2_1_2_3_1_1_2_2_1_1_2"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a>, <a class="txt" href="glib_005.html#E3:71_2_1_2_3_1_1_2_2"><i><font color="Green">E57</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_2_3_1_1_2_2_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:71_2_1_2_3_1_1_2_2_1_1_2_1"/>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:71_2_1_2_3_1_1_2_2_1_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_005.html#E2:71_2_1_2_3_1_1_2_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="ref" href="glib_001.html#D28">GLIB_001:def 28</a></i>;<br/><a NAME="E3:71_2_1_2_3_1_1_2_2_1_1_2_1"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K5">-</a> 2
 <b>by </b><i><a class="ref" href="heyting3.html#T1">HEYTING3:1</a></i>;<br/><b>hence </b><a NAME="E4:71_2_1_2_3_1_1_2_2_1_1_2_1"/>
contradiction
 ;<br/></div><b>end;</b></div><a NAME="E4:71_2_1_2_3_1_1_2_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E3:71_2_1_2_3_1_1_2_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><b>hence </b><a NAME="E5:71_2_1_2_3_1_1_2_2_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71_2_1_2_3_1_1_2"><i><font color="Green">E55</font></i></a>, <a class="txt" href="glib_005.html#E3:71_2_1_2_3_1_1_2_2"><i><font color="Green">E57</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:71_2_1_2_3_1_1_2_2"/>
contradiction
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:71_2_1_2_3_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E3:71_2_1_2_3"><i><font color="Green">E53</font></i></a>, <a class="txt" href="glib_005.html#E4:71_2_1_2_3_1_1_2"><i><font color="Green">E56</font></i></a>, <a class="txt" href="glib_005.html#E2:71"><i><font color="Green">E38</font></i></a>, <a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="txt" href="glib_005.html#E2:71_2_1_2_3"><i><font color="Green">E52</font></i></a>, <a class="ref" href="glib_005.html#D20" target="_self">Def20</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E7:71_2_1_2_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/></div><b>end;</b></div><b>then </b><i><font color="Green">E51</font></i>:  <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> = 
 <a href="uproots.html#K3">Sum</a> <font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="txt" href="glib_005.html#E7:71_2_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="glib_005.html#E9:71_2_1_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p0"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="glib_004.html#T9">GLIB_004:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span>

;<br/><a NAME="E12:71_2_1_2"/><i><font color="Green">E52</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_2_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:71_2_1_2_5"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:71_2_1_2_5"/><b>then </b><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E3:71_2_1_2_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="ref" href="glib_000.html#D28">GLIB_000:def 28</a></i>;<br/><a NAME="E4:71_2_1_2_5"/><b>then </b><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_2_5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:71_2_1_2_5_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="glib_001.html#K14">.edges()</a> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>17</sub></font> being   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>18</sub></font> being  <a href="abian.html#V1">odd</a> <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:71_2_1_2_5_1"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="glib_001.html#T104">GLIB_001:104</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_2_5_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_2_5_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:71_2_1_2_5_1_1_1"/>
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 </span><b>by </b><i><a class="txt" href="glib_005.html#E4:71_2_1_2_5"><i><font color="Green">E55</font></i></a>, <a class="txt" href="glib_005.html#E3:71_2_1_2_5_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="glib_000.html#D15">GLIB_000:def 15</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_2_5_1_1_1_1"><b>suppose </b></a><a NAME="E1:71_2_1_2_5_1_1_1_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:71_2_1_2_5_1_1_1_1"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a>, <a class="txt" href="glib_005.html#E3:71_2_1_2_5_1"><i><font color="Green">E56</font></i></a></i>;<br/><a NAME="E3:71_2_1_2_5_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="real_1.html#K5">-</a> 2 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 0
 <b>by </b><i><a class="txt" href="glib_005.html#E3:71_2_1_2_5_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E4:71_2_1_2_5_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_005.html#E2:71_2_1_2_5_1_1_1_1"><i><font color="Green">E58</font></i></a>, <a class="ref" href="glib_001.html#D28">GLIB_001:def 28</a></i>;<br/><b>hence </b><a NAME="E5:71_2_1_2_5_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="txt" href="glib_005.html#E1:71_2_1_2_5_1_1_1_1"><i><font color="Green">E57</font></i></a>, <a class="txt" href="glib_005.html#E3:71_2_1_2_5_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_2_1_2_5_1_1_1_2"><b>suppose </b></a><a NAME="E1:71_2_1_2_5_1_1_1_2"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:71_2_1_2_5_1_1_1_2"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a>, <a class="txt" href="glib_005.html#E3:71_2_1_2_5_1"><i><font color="Green">E56</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1_2_5_1_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:71_2_1_2_5_1_1_1_2_1"/>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:71_2_1_2_5_1_1_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_005.html#E2:71_2_1_2_5_1_1_1_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="glib_001.html#D28">GLIB_001:def 28</a></i>;<br/><a NAME="E3:71_2_1_2_5_1_1_1_2_1"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K5">-</a> 2
 <b>by </b><i><a class="ref" href="heyting3.html#T1">HEYTING3:1</a></i>;<br/><b>hence </b><a NAME="E4:71_2_1_2_5_1_1_1_2_1"/>
contradiction
 ;<br/></div><b>end;</b></div><a NAME="E4:71_2_1_2_5_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E3:71_2_1_2_5_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E5:71_2_1_2_5_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E6:71_2_1_2_5_1_1_1_2"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E3:71_2_1_2_5_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="glib_005.html#E3:71_2_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="glib_005.html#E4:71_2_1_2_5"><i><font color="Green">E55</font></i></a>, <a class="ref" href="glib_000.html#D16">GLIB_000:def 16</a></i>;<br/><a NAME="E7:71_2_1_2_5_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_005.html#E14:71"><i><font color="Green">E44</font></i></a>, <a class="txt" href="glib_005.html#E9:71"><i><font color="Green">E40</font></i></a>, <a class="ref" href="glib_001.html#D28">GLIB_001:def 28</a></i>;<br/><b>hence </b><a NAME="E8:71_2_1_2_5_1_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="txt" href="glib_005.html#E6:71_2_1_2_5_1_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="ref" href="glib_001.html#T18">GLIB_001:18</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:71_2_1_2_5_1"/>
contradiction
 ;<br/></div><b>end;</b></div><b>then </b><span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p2">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="glib_005.html#E2:71"><i><font color="Green">E38</font></i></a>, <a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="txt" href="glib_005.html#E2:71_2_1_2_5"><i><font color="Green">E54</font></i></a>, <a class="ref" href="glib_005.html#D20" target="_self">Def20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="glib_005.html#E13:71"><i><font color="Green">E43</font></i></a>, <a class="txt" href="glib_005.html#E2:71_2_1_2_5"><i><font color="Green">E54</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E7:71_2_1_2_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="glib_005.html#E1:71_2_1_2_5"><i><font color="Green">E53</font></i></a>, <a class="txt" href="glib_005.html#E12:71_2_1_2"><i><font color="Green">E52</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/></div><b>end;</b></div><a NAME="E14:71_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p2">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_005.html#E12:71_2_1_2"><i><font color="Green">E52</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E15:71_2_1_2"/><b>then </b>
 <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="uproots.html#K3">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_004.html#T7">GLIB_004:7</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></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 class="p1">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></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="uproots.html#K3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="glib_005.html#E11:71_2_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="glib_005.html#E3:71"><i><font color="Green">E39</font></i></a>, <a class="ref" href="glib_005.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K19">.edgesInto</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="uproots.html#K3">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_005.html#K1" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_circ.html#K3">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K20">.edgesOutOf</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <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#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span>
<b>by </b><i><a class="txt" href="glib_005.html#E1:71"><i><font color="Green">E37</font></i></a>, <a class="ref" href="glib_005.html#D8" target="_self">Def8</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E16:71"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <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#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_005.html#K9" target="_self">.tolerance()</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K12" target="_self">FF:AugmentPath</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></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>
 ;<br/>


</div>
