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<b>let </b><font color="Maroon">T</font> be  <a href="trees_9.html#V2">finite-branching</a> <a href="trees_1.html#NM1">Tree</a>;<br/>

<b>assume </b><a NAME="E1:20"/>
not <font color="Maroon">T</font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>

<b>then consider </b><font color="Maroon">C</font> being    <a href="trees_2.html#M1">Chain</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E3:20"/><i><font color="Green">E22</font></i>: 
not <font color="Maroon">C</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">B</font> being   <a href="trees_2.html#NM3">Branch</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E5:20"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="trees_2.html#T30">TREES_2:30</a></i>;<br/>
<a NAME="E6:20"/>
not <font color="Maroon">B</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i>, , <a class="ref" href="finset_1.html#T13">FINSET_1:13</a></i>;<br/>
<b>hence </b><a NAME="E7:20"/>
not for <font color="Olive">B</font> being  <a href="trees_2.html#NM3">Branch</a> of <font color="Maroon">T</font> holds  <font color="Olive">B</font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>


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