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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="trees_1.html#NM1">Tree</a>;<br/>

<b>assume </b><a NAME="E1:18_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="trees_2.html#V1">finite-order</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  <a href="trees_2.html#V1">finite-order</a> <a href="trees_1.html#NM1">Tree</a> ;<br/>
<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_9.html#D2" target="_self">TREES_9:def 2</a><br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/>
<a NAME="E4:18_1_1"/>
 <a href="trees_2.html#K1">succ</a> <font color="Maroon">c<sub>4</sub></font> is <a href="finset_1.html#V1">finite</a>
 
;<br/>
<b>hence </b><a NAME="E5:18_1_1"/>
 <a href="trees_2.html#K1">succ</a> <font color="Maroon">c<sub>3</sub></font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>


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