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<b>let </b><font color="Maroon">fT</font> be  <a href="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a>;<br/>

<a NAME="E1:68"/><i><font color="Green">E28</font></i>: 
 ex <font color="Olive">X</font> being   <a href="trees_1.html#M4" target="_self">AntiChain_of_Prefixes</a> of <font color="Maroon">fT</font> st <br/>(  <a href="trees_1.html#K7" target="_self">width</a> <font color="Maroon">fT</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Olive">X</font> &amp; ( for <font color="Olive">Y</font> being   <a href="trees_1.html#M4" target="_self">AntiChain_of_Prefixes</a> of <font color="Maroon">fT</font> holds   <a href="card_1.html#K4">card</a> <font color="Olive">Y</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Olive">X</font> ) )
 
<b>by </b><i><a class="ref" href="trees_1.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E2:68"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> is    <a href="trees_1.html#M4" target="_self">AntiChain_of_Prefixes</a> of <font color="Maroon">fT</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:68"/><b>then </b>
(  <a href="card_1.html#K4">card</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="trees_1.html#K7" target="_self">width</a> <font color="Maroon">fT</font> &amp;  <a href="card_1.html#K4">card</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> 1 )
 
<b>by </b><i><a class="ref" href="trees_1.html#T8" target="_self">Th8</a>, <a class="ref" href="card_1.html#T79">CARD_1:79</a></i>;<br/>
<b>hence </b><a NAME="E4:68"/>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="trees_1.html#K7" target="_self">width</a> <font color="Maroon">fT</font>
 ;<br/>


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