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

<span class="kw">let </span><font color="Maroon" title="c1">G2</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font></span>)</span><br/>  for <font color="Olive" title="b2">G1</font> being    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c1">G2</font>,<font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b3">v1</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b2">G1</font><br/>  for <font color="Olive" title="b4">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G2</font>  st <font color="Olive" title="b3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">v2</font> &amp; <font color="Olive" title="b3">v1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">V</font> holds <br/>( <font color="Olive" title="b3">v1</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 &amp; <font color="Olive" title="b3">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 &amp; <font color="Olive" title="b3">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">v2</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 2 )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font></span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">G1</font> being    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">V</font><br/>  for <font color="Olive" title="b2">v1</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b1">G1</font><br/>  for <font color="Olive" title="b3">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G2</font>  st <font color="Olive" title="b2">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v2</font> &amp; <font color="Olive" title="b2">v1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">V</font> holds <br/>( <font color="Olive" title="b2">v1</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 &amp; <font color="Olive" title="b2">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 &amp; <font color="Olive" title="b2">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">v2</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 2 )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">G1</font> be    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v1</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c3">G1</font><br/>  for <font color="Olive" title="b2">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G2</font>  st <font color="Olive" title="b1">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">v1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">V</font> holds <br/>( <font color="Olive" title="b1">v1</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 &amp; <font color="Olive" title="b1">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 &amp; <font color="Olive" title="b1">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v2</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 2 )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">v1</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c3">G1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G2</font>  st <font color="Maroon" title="c4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v2</font> &amp; <font color="Maroon" title="c4">v1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">V</font> holds <br/>( <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 &amp; <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 &amp; <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v2</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 2 )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">v2</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v2</font> &amp; <font color="Maroon" title="c4">v1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">V</font> implies ( <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 &amp; <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 &amp; <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 2 ) )</span><br/>









<span class="kw">assume </span><a NAME="E1:78"/>
( <font color="Maroon" title="c4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v2</font> &amp; <font color="Maroon" title="c4">v1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">V</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 &amp; <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 &amp; <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 2 )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:78"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
( <font color="Maroon" title="c6">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c3">G1</font> &amp;  not <font color="Maroon" title="c6">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> )
 <span class="kw">and </span><br/><a NAME="E4:78"/><span class="lab"><font color="Green" title="E35">A2</font></span>: 
<font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">and </span><br/><a NAME="E5:78"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
<font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">and </span><br/><a NAME="E6:78"/>
<font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesInOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesInOut()</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_012.html#T42" target="_self" onmouseover="rs('glib_012/T42')" onmouseout="rh()">Th42</a></span>;<br/>
<a NAME="E7:78"/>
 not <font color="Maroon" title="c6">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:78"><span class="lab"><font color="Green" title="E34">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><span class="lab"><font color="Green" title="E37">A4</font></span>: <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:78"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="card_2.html#T35" onmouseover="rs('card_2/T35')" onmouseout="rh()">CARD_2:35</a>, <a class="ref" href="zfmisc_1.html#T50" onmouseover="rs('zfmisc_1/T50')" onmouseout="rh()">ZFMISC_1:50</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T30" onmouseover="rs('card_1/T30')" onmouseout="rh()">CARD_1:30</a></span>
;<br/> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1 &amp; <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 2 )</span><br/>

<a NAME="E9:78"/>
 not <font color="Maroon" title="c6">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:78"><span class="lab"><font color="Green" title="E34">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:78"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="card_2.html#T35" onmouseover="rs('card_2/T35')" onmouseout="rh()">CARD_2:35</a>, <a class="ref" href="zfmisc_1.html#T50" onmouseover="rs('zfmisc_1/T50')" onmouseout="rh()">ZFMISC_1:50</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T30" onmouseover="rs('card_1/T30')" onmouseout="rh()">CARD_1:30</a></span>
;<br/> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 2</span><br/>

<span class="kw">hence </span><font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <span class="p1">(<span class="default">1 <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:78"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="card_2.html#T19" onmouseover="rs('card_2/T19')" onmouseout="rh()">CARD_2:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <span class="p2">(<span class="default">1 <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T19" onmouseover="rs('card_2/T19')" onmouseout="rh()">CARD_2:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> 2
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T19" onmouseover="rs('card_2/T19')" onmouseout="rh()">CARD_2:19</a></span>
;<br/> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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