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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green">E9</font></i>: 
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>1</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> is  <a href="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a>
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green">E10</font></i>: 
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>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> is  <a href="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D4" target="_self">TREES_3:def 4</a><br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D4" target="_self">TREES_3:def 4</a><br/>

<b>assume </b><a NAME="E3:13"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E4:13"/><b>then </b>
( not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> iff <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#T1">XBOOLE_0:1</a></i>;<br/>
<b>hence </b><a NAME="E5:13"/>
<font color="Maroon">c<sub>3</sub></font> is  <a href="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a>
 <b>by </b><i><a class="txt" href="trees_3.html#E1:13"><i><font color="Green">E9</font></i></a>, <a class="txt" href="trees_3.html#E2:13"><i><font color="Green">E10</font></i></a></i>;<br/>


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