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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="graph_1.html#V7" title="GRAPH_1:attr.7">finite</a> <a href="graph_1.html#NM1" title="GRAPH_1:NM.1">Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">v</font> be   <a href="graph_3.html#NM2" title="GRAPH_3:NM.2">Vertex</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>consider </b><font color="Maroon" title="c3">X</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E2:37"/><i><font color="Green" title="E28">A1</font></i>: 
for <font color="Olive" title="b1">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> iff ( <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c1">G</font> &amp; the <a href="graph_1.html#U3" title="GRAPH_1:sel.3">Source</a> of <font color="Maroon" title="c1">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> ) )
 <b>and </b><br/><a NAME="E3:37"/><i><font color="Green" title="E29">A2</font></i>: 
 <a href="graph_1.html#K5" title="GRAPH_1:func.5">EdgesOut</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="ref" href="graph_1.html#D21" title="GRAPH_1:def.21">GRAPH_1:def 21</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><a NAME="E1:37_1"/>
( <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_3.html#K3" title="GRAPH_3:func.3">Edges_Out</a> <font color="Maroon" title="c2">v</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c1">G</font> iff ( <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c1">G</font> &amp; the <a href="graph_1.html#U3" title="GRAPH_1:sel.3">Source</a> of <font color="Maroon" title="c1">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> ) )
 <b>by </b><i><a class="ref" href="graph_3.html#D2" target="_self" title="GRAPH_3:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E2:37_1"/>
( <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_3.html#K6" title="GRAPH_3:func.6">Edges_Out</a> <font color="Maroon" title="c2">v</font> iff <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> )
 <b>by </b><i><a class="txt" href="graph_3.html#E2:37"><i><font color="Green" title="E28">A1</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:37"/>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="graph_3.html#K6" title="GRAPH_3:func.6">Edges_Out</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K5" title="GRAPH_1:func.5">EdgesOut</a> <font color="Maroon" title="c2">v</font>
 <b>by </b><i><a class="txt" href="graph_3.html#E3:37"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>


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