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<b>let </b><font color="Maroon" title="c1">T</font> be  <a href="trees_9.html#V2" title="TREES_9:attr.2">finite-branching</a> <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c1">T</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> implies  ex <font color="Olive" title="b1">B</font> being  <a href="trees_2.html#NM3" title="TREES_2:NM.3">Branch</a> of <font color="Maroon" title="c1">T</font> st not <font color="Olive" title="b1">B</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )</span><br/>

<b>assume </b><a NAME="E1:20"/>
not <font color="Maroon" title="c1">T</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not for <font color="Olive" title="b1">B</font> being  <a href="trees_2.html#NM3" title="TREES_2:NM.3">Branch</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Olive" title="b1">B</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a></span><br/>

<b>then consider </b><font color="Maroon" title="c2">C</font> being    <a href="trees_2.html#M1" title="TREES_2:mode.1">Chain</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E3:20"/><i><font color="Green" title="E19">A1</font></i>: 
not <font color="Maroon" title="c2">C</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="ref" href="qc_lang4.html#T21" target="_self" title="QC_LANG4:th.21">Th21</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">B</font> being   <a href="trees_2.html#NM3" title="TREES_2:NM.3">Branch</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E5:20"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c2">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font>
 <b>by </b><i><a class="ref" href="trees_2.html#T30" title="TREES_2:th.30">TREES_2:30</a></i>;<br/>
<a NAME="E6:20"/>
not <font color="Maroon" title="c3">B</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="txt" href="#E3:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="#E5:20"><i><font color="Green" title="E20">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:20"/>
not for <font color="Olive" title="b1">B</font> being  <a href="trees_2.html#NM3" title="TREES_2:NM.3">Branch</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Olive" title="b1">B</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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