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<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="graph_1.html#V6" title="GRAPH_1:attr.6">finite</a>  <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">v</font> being  <a href="graph_3.html#NM2" title="GRAPH_3:NM.2">Vertex</a> of <font color="Maroon" title="c1">G</font> holds   <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="graph_3.html#K5" title="GRAPH_3:func.5">Edges_In</a> <font color="Olive" title="b1">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K6" title="GRAPH_1:func.6">EdgesIn</a> <font color="Olive" title="b1">v</font></span><br/><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="graph_3.html#K5" title="GRAPH_3:func.5">Edges_In</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#K6" title="GRAPH_1:func.6">EdgesIn</a> <font color="Maroon" title="c2">v</font></span><br/>



<span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E2:40"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
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="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G</font> &amp; the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</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> ) )
 <span class="kw">and </span><br/><a NAME="E3:40"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
 <a href="graph_1.html#K6" title="GRAPH_1:func.6">EdgesIn</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="graph_1.html#D21" title="GRAPH_1:def.21">GRAPH_1:def 21</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_3.html#K5" title="GRAPH_3:func.5">Edges_In</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> )</span><br/><a NAME="E1:40_1"/>
( <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_3.html#K2" title="GRAPH_3:func.2">Edges_In</a> <font color="Maroon" title="c2">v</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</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="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G</font> &amp; the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</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> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="graph_3.html#D1" target="_self" title="GRAPH_3:def.1">Def1</a></span>;<br/><span class="kw">hence </span><a NAME="E2:40_1"/>
( <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_3.html#K5" title="GRAPH_3:func.5">Edges_In</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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:40"><span class="lab"><font color="Green" title="E26">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:40"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="graph_3.html#K5" title="GRAPH_3:func.5">Edges_In</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#K6" title="GRAPH_1:func.6">EdgesIn</a> <font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:40"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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