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

<b>let </b><font color="Maroon" title="c1">D1</font>, <font color="Maroon" title="c2">D2</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">d1</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D1</font>;<br/><b>let </b><font color="Maroon" title="c4">d2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D2</font>;<br/><b>let </b><font color="Maroon" title="c5">F</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="trees_3.html#NM8" title="TREES_3:NM.8">DTree-set</a> of <font color="Maroon" title="c1">D1</font>,<font color="Maroon" title="c2">D2</font>;<br/><b>let </b><font color="Maroon" title="c6">F2</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="trees_3.html#M4" title="TREES_3:mode.4">DTree-set</a> of <font color="Maroon" title="c2">D2</font>;<br/><b>let </b><font color="Maroon" title="c7">p</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c5">F</font>;<br/><b>let </b><font color="Maroon" title="c8">p2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c6">F2</font>;<br/>















<b>assume </b><b>that </b><br/><a NAME="E1:50"/><i><font color="Green" title="E20">A1</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">p</font>
 <b>and </b><br/><a NAME="E2:50"/><i><font color="Green" title="E21">A2</font></i>: 
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">p</font> holds <br/>for <font color="Olive" title="b2">T</font> being  <a href="trees_3.html#NM7" title="TREES_3:NM.7">DecoratedTree</a> of <font color="Maroon" title="c1">D1</font>,<font color="Maroon" title="c2">D2</font>  st <font color="Olive" title="b2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> holds <br/><font color="Maroon" title="c8">p2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">T</font> <a href="trees_3.html#K11" title="TREES_3:func.11">`2</a> 
 ;<br/>

<b>set </b><font color="Maroon" title="c9">W</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c7">p</font>;<br/>
<b>set </b><font color="Maroon" title="c10">W2</font> = <font color="Maroon" title="c4">d2</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c8">p2</font>;<br/>
<a NAME="E3:50"/><i><font color="Green" title="E22">A3</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">p</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <font color="Maroon" title="c8">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p2</font> )
 
<b>by </b><i><a class="txt" href="trees_4.html#E1:50"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a>, <a class="ref" href="trees_3.html#T40" title="TREES_3:th.40">TREES_3:40</a></i>;<br/>
<a NAME="E4:50"/><b>then </b><i><font color="Green" title="E23">A4</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <font color="Maroon" title="c8">p2</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">p</font> )
 
<b>by </b><i><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:50_1"/><i><font color="Green" title="E24">A5</font></i>: 
<font color="Maroon" title="c11">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">p</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c12">T</font> = <font color="Maroon" title="c7">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font> as    <a href="trees_3.html#M5" title="TREES_3:mode.5">Element</a> of <font color="Maroon" title="c5">F</font> <b>by </b><i><a class="txt" href="trees_4.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/><a NAME="E3:50_1"/>
<font color="Maroon" title="c8">p2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">T</font> <a href="trees_3.html#K11" title="TREES_3:func.11">`2</a> 
 <b>by </b><i><a class="txt" href="trees_4.html#E2:50"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="trees_4.html#E1:50_1"><i><font color="Green" title="E24">A5</font></i></a></i>;<br/><a NAME="E4:50_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c12">T</font> &amp; <span class="p1">(<span class="default"><a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <font color="Maroon" title="c8">p2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">T</font> <a href="trees_3.html#K11" title="TREES_3:func.11">`2</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="trees_4.html#E1:50"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="trees_4.html#E1:50_1"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="funct_6.html#T31" title="FUNCT_6:th.31">FUNCT_6:31</a></i>;<br/><b>hence </b><a NAME="E5:50_1"/>
<span class="p1">(<span class="default"><a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <font color="Maroon" title="c8">p2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font>
 <b>by </b><i><a class="ref" href="trees_4.html#T24" target="_self" title="TREES_4:th.24">Th24</a></i>;<br/></div><b>end;</b></div>
<a NAME="E6:50"/><b>then </b><i><font color="Green" title="E24">A6</font></i>: 
 <a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <font color="Maroon" title="c8">p2</font>
 
<b>by </b><i><a class="txt" href="trees_4.html#E4:50"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="finseq_1.html#T17" title="FINSEQ_1:th.17">FINSEQ_1:17</a></i>;<br/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="trees_3.html#K11" title="TREES_3:func.11">`2</a> </span>)</span> = 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c7">p</font></span>)</span>
<b>by </b><i><a class="ref" href="trees_4.html#T24" target="_self" title="TREES_4:th.24">Th24</a></i>
<br/>.= 
 <a href="trees_3.html#K13" title="TREES_3:func.13">tree</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <font color="Maroon" title="c7">p</font></span>)</span>
<b>by </b><i><a class="ref" href="trees_4.html#T10" target="_self" title="TREES_4:th.10">Th10</a></i>
;<br/>
<b>hence </b><a NAME="E8:50"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="trees_3.html#K11" title="TREES_3:func.11">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">d2</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c8">p2</font></span>)</span>
 <b>by </b><i><a class="txt" href="trees_4.html#E6:50"><i><font color="Green" title="E24">A6</font></i></a>, <a class="ref" href="trees_4.html#T10" target="_self" title="TREES_4:th.10">Th10</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_4.html#D1" target="_self" title="TREES_4:def.1">TREES_4:def 1</a><br/>

<b>let </b><font color="Maroon" title="c11">x</font> be   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="trees_3.html#K11" title="TREES_3:func.11">`2</a> </span>)</span>;<br/>

<b>reconsider </b><font color="Maroon" title="c12">a</font> = <font color="Maroon" title="c11">x</font> as   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c7">p</font></span>)</span> <b>by </b><i><a class="ref" href="trees_4.html#T24" target="_self" title="TREES_4:th.24">Th24</a></i>;<br/>
<a NAME="E10:50"/><i><font color="Green" title="E25">A7</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="trees_3.html#K11" title="TREES_3:func.11">`2</a> </span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c12">a</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> 
 
<b>by </b><i><a class="ref" href="trees_3.html#T41" title="TREES_3:th.41">TREES_3:41</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:50_3"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c11">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_3_1"><b>suppose </b></a><a NAME="E1:50_3_1"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:50_3_1"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">d2</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c8">p2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">d2</font> )
 <b>by </b><i><a class="ref" href="trees_4.html#D4" target="_self" title="TREES_4:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E3:50_3_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="trees_3.html#K11" title="TREES_3:func.11">`2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">d2</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c8">p2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
 <b>by </b><i><a class="txt" href="trees_4.html#E10:50"><i><font color="Green" title="E25">A7</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_3_2"><b>suppose </b></a><a NAME="E1:50_3_2"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c13">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <font color="Maroon" title="c14">T</font> being   <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>, <font color="Maroon" title="c15">q</font> being   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c14">T</font><b> such that </b><br/><a NAME="E3:50_3_2"/><i><font color="Green" title="E26">A8</font></i>: 
( <font color="Maroon" title="c13">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">p</font> &amp; <font color="Maroon" title="c14">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> &amp; <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c13">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c15">q</font> )
 <b>by </b><i><a class="ref" href="trees_4.html#T11" target="_self" title="TREES_4:th.11">Th11</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c16">T</font> = <font color="Maroon" title="c14">T</font> as    <a href="trees_3.html#M5" title="TREES_3:mode.5">Element</a> of <font color="Maroon" title="c5">F</font> <b>by </b><i><a class="txt" href="trees_4.html#E3:50_3_2"><i><font color="Green" title="E26">A8</font></i></a>, <a class="txt" href="trees_4.html#E6"><i><font color="Green" title="E5">Lm3</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c17">q</font> = <font color="Maroon" title="c15">q</font> as   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">T</font> <a href="trees_3.html#K11" title="TREES_3:func.11">`2</a> </span>)</span> <b>by </b><i><a class="ref" href="trees_4.html#T24" target="_self" title="TREES_4:th.24">Th24</a></i>;<br/><a NAME="E6:50_3_2"/>
<font color="Maroon" title="c13">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">p</font>
 <b>by </b><i><a class="txt" href="trees_4.html#E3:50_3_2"><i><font color="Green" title="E26">A8</font></i></a>, <a class="txt" href="trees_4.html#E5"><i><font color="Green" title="E4">Lm2</font></i></a></i>;<br/><a NAME="E7:50_3_2"/><b>then </b>
<font color="Maroon" title="c8">p2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">T</font> <a href="trees_3.html#K11" title="TREES_3:func.11">`2</a> 
 <b>by </b><i><a class="txt" href="trees_4.html#E2:50"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="trees_4.html#E3:50_3_2"><i><font color="Green" title="E26">A8</font></i></a></i>;<br/><a NAME="E8:50_3_2"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">T</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">q</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">d2</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c8">p2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">T</font> <a href="trees_3.html#K11" title="TREES_3:func.11">`2</a> </span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c17">q</font> )
 <b>by </b><i><a class="txt" href="trees_4.html#E3:50"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="trees_4.html#E3:50_3_2"><i><font color="Green" title="E26">A8</font></i></a>, <a class="ref" href="trees_4.html#T12" target="_self" title="TREES_4:th.12">Th12</a></i>;<br/><b>hence </b><a NAME="E9:50_3_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="trees_3.html#K11" title="TREES_3:func.11">`2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">d2</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c8">p2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
 <b>by </b><i><a class="txt" href="trees_4.html#E10:50"><i><font color="Green" title="E25">A7</font></i></a>, <a class="ref" href="trees_3.html#T41" title="TREES_3:th.41">TREES_3:41</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
