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<b>let </b><font color="Maroon">T</font> be   <a href="trees_2.html#NM4">DecoratedTree</a>;<br/><b>let </b><font color="Maroon">T1</font> be   <a href="trees_2.html#NM4">DecoratedTree</a>;<br/><b>let </b><font color="Maroon">P</font> be    <a href="trees_1.html#M4">AntiChain_of_Prefixes</a> of  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font>;<br/>





<b>assume </b><a NAME="E1:14"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>let </b><font color="Maroon">q</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E2:14"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="trees_a.html#K3" target="_self">tree</a> <font color="Maroon">T</font>,<font color="Maroon">P</font>,<font color="Maroon">T1</font></span>)</span>
 ;<br/>

<a NAME="E3:14"/><b>then </b>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="trees_a.html#K1" target="_self">tree</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font></span>)</span>,<font color="Maroon">P</font>,<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T1</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:14"/>
( 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">q</font> &amp; <span class="p1">(<span class="default"><a href="trees_a.html#K3" target="_self">tree</a> <font color="Maroon">T</font>,<font color="Maroon">P</font>,<font color="Maroon">T1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">q</font> ) or  ex <font color="Olive">p</font>, <font color="Olive">r</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Olive">r</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T1</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Olive">p</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">r</font> &amp; <span class="p1">(<span class="default"><a href="trees_a.html#K3" target="_self">tree</a> <font color="Maroon">T</font>,<font color="Maroon">P</font>,<font color="Maroon">T1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">r</font> ) )
 <b>by </b><i/>;<br/>


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