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<b>let </b><font color="Maroon" title="c2">B</font> be    <a href="trees_2.html#M1" title="TREES_2:mode.1">Chain</a> of <font color="Maroon" title="c1">W</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">B</font> is <a href="trees_2.html#V2" title="TREES_2:attr.2">Branch-like</a> implies  not <font color="Maroon" title="c2">B</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )</span><br/>

<b>assume </b><a NAME="E1:33_1_1"/><i><font color="Green" title="E14">A1</font></i>: 
( <font color="Maroon" title="c2">B</font> is <a href="trees_2.html#V2" title="TREES_2:attr.2">Branch-like</a> &amp; <font color="Maroon" title="c2">B</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>consider </b><font color="Maroon" title="c3">t</font> being    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Maroon" title="c1">W</font>;<br/>
<a NAME="E3:33_1_1"/>
( <font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font> &amp; ( for <font color="Olive" title="b1">q</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> holds <br/><font color="Olive" title="b1">q</font> <a href="trees_1.html#NR3" title="TREES_1:NR.3">is_a_proper_prefix_of</a> <font color="Maroon" title="c3">t</font> ) )
 
<b>by </b><i><a class="txt" href="trees_2.html#E1:33_1_1"><i><font color="Green" title="E14">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:33_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="trees_2.html#E1:33_1_1"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="trees_2.html#D7" target="_self" title="TREES_2:def.7">Def7</a></i>; <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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