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<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">X2</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X1</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:44"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">X2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X1</font>
 ;<br/>

<b>set </b><font color="Maroon">n12I</font> =  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="graph_3.html#K2" target="_self">Edges_In</a> <font color="Maroon">v</font>,<span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">X2</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">n12O</font> =  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="graph_3.html#K3" target="_self">Edges_Out</a> <font color="Maroon">v</font>,<span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">X2</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">n1I</font> =  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="graph_3.html#K2" target="_self">Edges_In</a> <font color="Maroon">v</font>,<font color="Maroon">X1</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">n2I</font> =  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="graph_3.html#K2" target="_self">Edges_In</a> <font color="Maroon">v</font>,<font color="Maroon">X2</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">n1O</font> =  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="graph_3.html#K3" target="_self">Edges_Out</a> <font color="Maroon">v</font>,<font color="Maroon">X1</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">n2O</font> =  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="graph_3.html#K3" target="_self">Edges_Out</a> <font color="Maroon">v</font>,<font color="Maroon">X2</font></span>)</span>;<br/>
<a NAME="E2:44"/><i><font color="Green">E32</font></i>: 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="graph_3.html#K2" target="_self">Edges_In</a> <font color="Maroon">v</font>,<span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">X2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</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#K2" target="_self">Edges_In</a> <font color="Maroon">v</font>,<font color="Maroon">X1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</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#K2" target="_self">Edges_In</a> <font color="Maroon">v</font>,<font color="Maroon">X2</font></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:44"/>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="graph_3.html#K3" target="_self">Edges_Out</a> <font color="Maroon">v</font>,<span class="p2">(<span class="default"><font color="Maroon">X1</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">X2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</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">X1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</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">X2</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="txt" href="graph_3.html#E2:44"><i><font color="Green">E32</font></i></a></i>;<br/>
<a NAME="E4:44"/><b>then </b>
<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>,<span class="p3">(<span class="default"><font color="Maroon">X1</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">X2</font></span>)</span></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>,<span class="p3">(<span class="default"><font color="Maroon">X1</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">X2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><a href="graph_3.html#K2" target="_self">Edges_In</a> <font color="Maroon">v</font>,<font color="Maroon">X1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><a href="graph_3.html#K3" target="_self">Edges_Out</a> <font color="Maroon">v</font>,<font color="Maroon">X1</font></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="card_1.html#K4">card</a> <span class="p3">(<span class="default"><a href="graph_3.html#K2" target="_self">Edges_In</a> <font color="Maroon">v</font>,<font color="Maroon">X2</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><a href="graph_3.html#K3" target="_self">Edges_Out</a> <font color="Maroon">v</font>,<font color="Maroon">X2</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:44"/>
 <a href="graph_3.html#K7" target="_self">Degree</a> <font color="Maroon">v</font>,<span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">X2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="graph_3.html#K7" target="_self">Degree</a> <font color="Maroon">v</font>,<font color="Maroon">X1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="graph_3.html#K7" target="_self">Degree</a> <font color="Maroon">v</font>,<font color="Maroon">X2</font></span>)</span>
 ;<br/>


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