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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">G</font> be  <a href="graph_1.html#V7">finite</a> <a href="graph_1.html#NM1">Graph</a>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="graph_3.html#NM2">Vertex</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">v1</font> be   <a href="graph_3.html#NM2">Vertex</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">v2</font> be   <a href="graph_3.html#NM2">Vertex</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">v'</font> be   <a href="graph_3.html#NM2">Vertex</a> of <span class="p1">(<span class="default"><a href="graph_3.html#K8" target="_self">AddNewEdge</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font></span>)</span>;<br/>











<b>assume </b><a NAME="E1:65"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">v'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">v1</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">v2</font> )
 ;<br/>

<b>thus </b> <a href="graph_3.html#K7" target="_self">Degree</a> <font color="Maroon">v'</font>,<font color="Maroon">X</font> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="graph_3.html#K2" target="_self">Edges_In</a> <font color="Maroon">v</font>,<font color="Maroon">X</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="graph_3.html#K3" target="_self">Edges_Out</a> <font color="Maroon">v'</font>,<font color="Maroon">X</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
 <a href="graph_3.html#K7" target="_self">Degree</a> <font color="Maroon">v</font>,<font color="Maroon">X</font>
<b>by </b><i>, </i>
;<br/>


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