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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] means the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:35_1_1"/><i><font color="Green">E19</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="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<a NAME="E3:35_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="graph_1.html#E2:35_1_1"><i><font color="Green">E19</font></i></a></i>;<br/>
<a NAME="E4:35_1_1"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font> &amp; the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font> is <a href="finset_1.html#V1">finite</a> )
 
<b>by </b><i><a class="ref" href="graph_1.html#D8" target="_self">Def8</a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i><a class="ref" href="finset_1.html#T13">FINSET_1:13</a></i>;<br/>
<b>take </b>
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>thus </b><a NAME="E6:35_1_1"/>
( ( 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>6</sub></font> iff ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font> &amp; the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> ) ) ) &amp;  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="graph_1.html#E2:35_1_1"><i><font color="Green">E19</font></i></a></i>;<br/>


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