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<b>set </b><font color="Maroon">T</font> =  <a href="trees_1.html#K2">elementary_tree</a> 0;<br/>
<b>let </b><font color="Maroon">t</font> be    <a href="trees_1.html#M1">Element</a> of  <a href="trees_1.html#K2">elementary_tree</a> 0; <i><font color="Red">:: according to </font></i><a class="ref" href="bintree1.html#D2" target="_self">BINTREE1:def 2</a><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">s</font> be    <a href="trees_4.html#M1">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:4_1"/>
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="trees_1.html#K2">elementary_tree</a> 0
 ;<br/><a NAME="E2:4_1"/><b>then </b>
( <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a>, <a class="ref" href="trees_1.html#T56">TREES_1:56</a></i>;<br/><b>hence </b><a NAME="E3:4_1"/>
not <font color="Maroon">t</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">s</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:4"/>
( not <font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="trees_1.html#K3">Leaves</a> <span class="p1">(<span class="default"><a href="trees_1.html#K2">elementary_tree</a> 0</span>)</span> implies  <a href="trees_2.html#K1">succ</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="lang1.html#K3">&lt;*</a><span class="default">0</span><a href="lang1.html#K3">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="lang1.html#K3">&lt;*</a><span class="default">1</span><a href="lang1.html#K3">*&gt;</a></span></span>)</span></span><a href="tarski.html#K2">}</a></span> )
 <b>by </b><i><a class="ref" href="trees_1.html#D8">TREES_1:def 8</a></i>;<br/>


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