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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   <a href="trees_9.html#V1" title="TREES_9:attr.1">finite-branching</a>  <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E1:23"/>
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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E3:23"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
not <font color="Maroon" title="c2">C</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang4.html#T21" target="_self" title="QC_LANG4:th.21">Th21</a></span>;<br/>
<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E5:23"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="trees_2.html#T30" title="TREES_2:th.30">TREES_2:30</a></span>;<br/>
<a NAME="E6:23"/>
not <font color="Maroon" title="c3">B</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E5:23"><span class="lab"><font color="Green" title="E20">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:23"/>
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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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