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<b>let </b><font color="Maroon">T</font> be   <a href="trees_1.html#NM1">Tree</a>;<br/><b>let </b><font color="Maroon">P</font> be    <a href="trees_1.html#M4">AntiChain_of_Prefixes</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>





<b>assume </b><a NAME="E1:4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">t1</font> where <font color="Olive">t1</font> is    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">T</font> : for <font color="Olive">p</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> holds <br/> not <font color="Olive">p</font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Olive">t1</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">t'</font> being    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E3:4"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t'</font> &amp; ( for <font color="Olive">p</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> holds <br/> not <font color="Olive">p</font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">t'</font> ) )
 ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:4_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 ;<br/><a NAME="E2:4_1"/><b>then </b>
not <font color="Maroon">p</font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">t'</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:4_1"/>
not <font color="Maroon">p</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">t'</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">t1</font> where <font color="Olive">t1</font> is    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">T</font> : for <font color="Olive">p</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> holds <br/> not <font color="Olive">p</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Olive">t1</font> </span>}</span> 
 <b>by </b><i/>;<br/>


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