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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="trees_1.html#K6">height</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E1:149"/><i><font color="Green">E61</font></i>: 
(  <a href="trees_3.html#K14" target="_self">^</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="trees_3.html#K13" target="_self">tree</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T55">FINSEQ_1:55</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:149"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being <a href="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> holds <br/> <a href="trees_1.html#K6">height</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="trees_1.html#K6">height</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:149"/>
 <a href="trees_1.html#K6">height</a> <span class="p1">(<span class="default"><a href="trees_3.html#K14" target="_self">^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="trees_1.html#K6">height</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="trees_3.html#E1:149"><i><font color="Green">E61</font></i></a>, <a class="ref" href="trees_3.html#T82" target="_self">Th82</a></i>;<br/>


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