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

<a NAME="E1:20_1"/><i><font color="Green">E12</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">F<sub>1</sub></font>() st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K6">Terminals</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">P<sub>1</sub></font>[ <a href="trees_4.html#K2">root-tree</a> <font color="Olive">b<sub>1</sub></font>]
 
<b>by </b><i><a class="txt" href="bintree1.html#E1:20"><i><font color="Green">E10</font></i></a></i>;<br/>
<a NAME="E2:20_1"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">F<sub>1</sub></font>()<br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">F<sub>1</sub></font>() st <font color="Olive">b<sub>1</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1">roots</a> <font color="Olive">b<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="trees_2.html#NM6">DecoratedTree</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>3</sub></font>] ) holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Olive">b<sub>2</sub></font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">F<sub>1</sub></font>();<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:20_1_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1">roots</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:20_1_1"/><i><font color="Green">E15</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="trees_2.html#NM6">DecoratedTree</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 ;<br/>

<a NAME="E3:20_1_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is   <a href="dtconstr.html#NM3">NonTerminal</a> of <font color="Maroon">F<sub>1</sub></font>()
 
<b>by </b><i><a class="txt" href="bintree1.html#E1:20_1_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="bintree1.html#T12" target="_self">Th12</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> being    <a href="dtconstr.html#M1">Element</a> of  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E5:20_1_1"/><i><font color="Green">E17</font></i>: 
 <a href="dtconstr.html#K1">roots</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="bintree1.html#K1" target="_self">root-label</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="bintree1.html#K1" target="_self">root-label</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="lang1.html#K4">*&gt;</a></span>
 <b>and </b><br/><a NAME="E6:20_1_1"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> 2 &amp; <font color="Maroon">c<sub>1</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="trees_4.html#K10">-tree</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="bintree1.html#E1:20_1_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="bintree1.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E7:20_1_1"/>
( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>3</sub></font>] &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>4</sub></font>] )
 
<b>by </b><i><a class="txt" href="bintree1.html#E2:20_1_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="bintree1.html#E6:20_1_1"><i><font color="Green">E18</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:20_1_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>1</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">c<sub>2</sub></font>]
 <b>by </b><i><a class="txt" href="bintree1.html#E2:20"><i><font color="Green">E11</font></i></a>, <a class="txt" href="bintree1.html#E1:20_1_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="bintree1.html#E3:20_1_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="bintree1.html#E5:20_1_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="bintree1.html#E6:20_1_1"><i><font color="Green">E18</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:20_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="trees_2.html#NM6">DecoratedTree</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="dtconstr.html#S7">DTCONSTR:sch 7</a>(<a class="txt" href="bintree1.html#E1:20_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="bintree1.html#E2:20_1"><i><font color="Green">E13</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:20_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="dtconstr.html#M1">Element</a> of  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">F<sub>1</sub></font>() holds <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 ;<br/>


</div>
