<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>set </b><font color="Maroon">p</font> = <font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p1">(<span class="default"><a href="trees_1.html#K2">elementary_tree</a> 0</span>)</span>;<br/>
<b>set </b><font color="Maroon">T</font> =  <a href="trees_3.html#K13">tree</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2">(<span class="default"><a href="trees_1.html#K2">elementary_tree</a> 0</span>)</span></span>)</span>;<br/>
<b>assume </b><a NAME="E1:16"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font>
 ;<br/>

<a NAME="E2:16"/><b>then </b>
( <font color="Maroon">j</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> &amp; 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">j</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2">(<span class="default"><a href="trees_1.html#K2">elementary_tree</a> 0</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> )
 
<b>by </b><i><a class="ref" href="finseq_2.html#T69">FINSEQ_2:69</a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E3:16"/><b>then </b>
(  <a href="trees_1.html#K2">elementary_tree</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="trees_3.html#K13">tree</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2">(<span class="default"><a href="trees_1.html#K2">elementary_tree</a> 0</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="trees_3.html#K13">tree</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p3">(<span class="default"><a href="trees_1.html#K2">elementary_tree</a> 0</span>)</span></span>)</span></span>)</span> <a href="trees_1.html#K4">|</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">j</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2">(<span class="default"><a href="trees_1.html#K2">elementary_tree</a> 0</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; <font color="Maroon">j</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">i</font> )
 
<b>by </b><i>, <a class="ref" href="trees_3.html#T52">TREES_3:52</a>, <a class="ref" href="trees_3.html#T57">TREES_3:57</a></i>;<br/>
<b>hence </b><a NAME="E4:16"/>
<span class="p1">(<span class="default"><a href="trees_1.html#K2">elementary_tree</a> <font color="Maroon">i</font></span>)</span> <a href="trees_1.html#K4">|</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">j</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="trees_1.html#K2">elementary_tree</a> 0
 <b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>


</div>
