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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="sgraph1.html#M1" target="_self">SimpleGraph</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:40"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="sgraph1.html#U1" target="_self">SEdges</a> of <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="sgraph1.html#K4" target="_self">degree</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<b>assume </b><a NAME="E2:40"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font> being  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:40"/><i><font color="Green">E25</font></i>: 
( ( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> iff ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="sgraph1.html#U1" target="_self">SEdges</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) ) ) &amp;  <a href="sgraph1.html#K4" target="_self">degree</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="sgraph1.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E5:40"/>
not <font color="Maroon">c<sub>5</sub></font> is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i><a class="txt" href="sgraph1.html#E1:40"><i><font color="Green">E23</font></i></a>, <a class="txt" href="sgraph1.html#E2:40"><i><font color="Green">E24</font></i></a>, <a class="txt" href="sgraph1.html#E4:40"><i><font color="Green">E25</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">E23</font></i></a>, <a class="txt" href="sgraph1.html#E4:40"><i><font color="Green">E25</font></i></a>, <a class="ref" href="card_2.html#T59">CARD_2:59</a></i>;<br/>


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