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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">g</font> be    <a href="sgraph1.html#M1" title="SGRAPH1:mode.1">SimpleGraph</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<b>assume </b><a NAME="E1:40"/><i><font color="Green" title="E23">A1</font></i>: 
( <font color="Maroon" title="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">g</font> &amp; <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="sgraph1.html#U1" title="SGRAPH1:sel.1">SEdges</a> of <font color="Maroon" title="c2">g</font> &amp;  <a href="sgraph1.html#K4" title="SGRAPH1:func.4">degree</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/>

<b>assume </b><a NAME="E2:40"/><i><font color="Green" title="E24">A2</font></i>: 
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">e</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">Y</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="E4:40"/><i><font color="Green" title="E25">A3</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="c5">Y</font> iff ( <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="sgraph1.html#U1" title="SGRAPH1:sel.1">SEdges</a> of <font color="Maroon" title="c2">g</font> &amp; <font color="Maroon" title="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">z</font> ) ) ) &amp;  <a href="sgraph1.html#K4" title="SGRAPH1:func.4">degree</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c3">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="c5">Y</font> )
 <b>by </b><i><a class="ref" href="sgraph1.html#D11" target="_self" title="SGRAPH1:def.11">Def11</a></i>;<br/>
<a NAME="E5:40"/>
not <font color="Maroon" title="c5">Y</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="txt" href="sgraph1.html#E1:40"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="sgraph1.html#E2:40"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="sgraph1.html#E4:40"><i><font color="Green" title="E25">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:40"/>
contradiction
 <b>by </b><i><a class="txt" href="sgraph1.html#E1:40"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="sgraph1.html#E4:40"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a></i>;<br/>


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