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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="trees_2.html#V1" target="_self">finite-order</a> <a href="trees_1.html#NM1">Tree</a>;<br/>

<a NAME="E1:48"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="trees_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds  <a href="trees_2.html#K1" target="_self">succ</a> <font color="Olive">b<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 
;<br/>
<b>hence </b><a NAME="E2:48"/>
( ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a>ex <font color="Olive">b<sub>2</sub></font> being <a href="finset_1.html#V1">finite</a>  <a href="trees_2.html#M1" target="_self">Chain</a> of <font color="Maroon">c<sub>1</sub></font> st  <a href="card_1.html#K4">card</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> ) implies ex <font color="Olive">b<sub>1</sub></font> being   <a href="trees_2.html#M1" target="_self">Chain</a> of <font color="Maroon">c<sub>1</sub></font> st not <font color="Olive">b<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a> )
 <b>by </b><i><a class="ref" href="trees_2.html#T31" target="_self">Th31</a></i>;<br/>


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