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<b>let </b><font color="Maroon">q1</font> be  <a href="funct_1.html#V2">one-to-one</a>  <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">t</font>, <font color="Maroon">q2</font> be  <a href="funct_1.html#V2">one-to-one</a>  <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">t</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:29_1_2"/><i><font color="Green">E61</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q1</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="trees_2.html#K1">succ</a> <font color="Maroon">p</font></span>)</span> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">q1</font> <a href="hidden.html#R1">=</a>  <a href="trees_2.html#K1">succ</a> <font color="Maroon">p</font> )
 <b>and </b><br/><a NAME="E2:29_1_2"/><i><font color="Green">E62</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q1</font> holds <br/><font color="Maroon">q1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">i</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>and </b><br/><a NAME="E3:29_1_2"/><i><font color="Green">E63</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q2</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="trees_2.html#K1">succ</a> <font color="Maroon">p</font></span>)</span> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">q2</font> <a href="hidden.html#R1">=</a>  <a href="trees_2.html#K1">succ</a> <font color="Maroon">p</font> )
 <b>and </b><br/><a NAME="E4:29_1_2"/><i><font color="Green">E64</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q2</font> holds <br/><font color="Maroon">q2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">i</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 ;<br/>

<a NAME="E5:29_1_2"/><i><font color="Green">E67</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">q1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="trees_2.html#K1">succ</a> <font color="Maroon">p</font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">q2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="trees_2.html#K1">succ</a> <font color="Maroon">p</font></span>)</span></span>)</span> )
 
<b>by </b><i>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:29_1_2_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="trees_2.html#K1">succ</a> <font color="Maroon">p</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:29_1_2_1"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q1</font> )
 <b>by </b><i>, </i>;<br/><b>thus </b><font color="Maroon">q1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> = 
<font color="Maroon">p</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">n</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">q2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i>, , , </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:29_1_2"/>
<font color="Maroon">q1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q2</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>;<br/>


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