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

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] means <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">1,5</span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>
<b>consider </b><font color="Maroon">c<sub>1</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="lang1.html#V1">strict</a> <a href="bintree1.html#V3">binary</a>  <a href="lang1.html#L1">DTConstrStr</a> <b> such that </b><br/><a NAME="E2:3_1_1"/><i><font color="Green">E5</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">1,5</span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>and </b><br/><a NAME="E3:3_1_1"/><i><font color="Green">E6</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="lang1.html#R1">==&gt;</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>] )
 <b>from </b><i><a class="ref" href="bintree1.html#S1">BINTREE1:sch 1</a>();<br/></i>
<a NAME="E4:3_1_1"/><i><font color="Green">E7</font></i>: 
 <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> : for <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> holds not <font color="Olive">b<sub>1</sub></font> <a href="lang1.html#R1">==&gt;</a> <font color="Olive">b<sub>2</sub></font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="lang1.html#D2">LANG1:def 2</a></i>;<br/>
<a NAME="E5:3_1_1"/><i><font color="Green">E8</font></i>: 
 <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:3_1_1_1"/>
 <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:3_1_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:3_1_1_1_1"/><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> holds not <font color="Maroon">c<sub>3</sub></font> <a href="lang1.html#R1">==&gt;</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="scm_comp.html#E4:3_1_1"><i><font color="Green">E7</font></i></a></i>;<br/>
<b>assume </b><a NAME="E4:3_1_1_1_1"/>
not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/>

<a NAME="E5:3_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">1,5</span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="scm_comp.html#E2:3_1_1"><i><font color="Green">E5</font></i></a>, <a class="txt" href="scm_comp.html#E3:3_1_1_1_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E6:3_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="lang1.html#R1">==&gt;</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K4">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="scm_comp.html#E3:3_1_1"><i><font color="Green">E6</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:3_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scm_comp.html#E3:3_1_1_1_1"><i><font color="Green">E9</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:3_1_1_1"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="scm_comp.html#E2:3_1_1"><i><font color="Green">E5</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>assume </b><a NAME="E4:3_1_1_1"/>
not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E6:3_1_1_1"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="lang1.html#R1">==&gt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="scm_comp.html#E4:3_1_1"><i><font color="Green">E7</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E8:3_1_1_1"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="lang1.html#K4">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scm_comp.html#E6:3_1_1_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="bintree1.html#D4">BINTREE1:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E10:3_1_1_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scm_comp.html#E2:3_1_1_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="ami_2.html#D2">AMI_2:def 2</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1;<br/>
<a NAME="E11:3_1_1_1"/>
0 <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 </span>}</span> 
 
;<br/>
<a NAME="E12:3_1_1_1"/><b>then </b><i><font color="Green">E13</font></i>: 
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="scm_comp.html#E10:3_1_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="axioms.html#T30">AXIOMS:30</a></i>;<br/>
<a NAME="E13:3_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">1,5</span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="scm_comp.html#E3:3_1_1"><i><font color="Green">E6</font></i></a>, <a class="txt" href="scm_comp.html#E6:3_1_1_1"><i><font color="Green">E10</font></i></a>, <a class="txt" href="scm_comp.html#E8:3_1_1_1"><i><font color="Green">E11</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E15:3_1_1_1"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> 1 &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> 5 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T103">ZFMISC_1:103</a></i>;<br/>
<a NAME="E16:3_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="tarski.html#K2">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>9</sub></font></span><a href="tarski.html#K1">}</a></span></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="txt" href="scm_comp.html#E15:3_1_1_1"><i><font color="Green">E14</font></i></a></i>;<br/>
<b>hence </b><a NAME="E17:3_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scm_comp.html#E12:3_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:3_1_1"/><i><font color="Green">E9</font></i>: 
 <a href="lang1.html#K6">NonTerminals</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> : ex <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Olive">b<sub>1</sub></font> <a href="lang1.html#R1">==&gt;</a> <font color="Olive">b<sub>2</sub></font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="lang1.html#D3">LANG1:def 3</a></i>;<br/>
<a NAME="E7:3_1_1"/><i><font color="Green">E10</font></i>: 
 <a href="lang1.html#K6">NonTerminals</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">1,5</span><a href="zfmisc_1.html#K2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_1_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:3_1_1_2"/>
 <a href="lang1.html#K6">NonTerminals</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">1,5</span><a href="zfmisc_1.html#K2">:]</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:3_1_1_2_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K6">NonTerminals</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:3_1_1_2_1"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; ex <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">c<sub>3</sub></font> <a href="lang1.html#R1">==&gt;</a> <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="scm_comp.html#E6:3_1_1"><i><font color="Green">E9</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E5:3_1_1_2_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="lang1.html#R1">==&gt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="scm_comp.html#E3:3_1_1_2_1"><i><font color="Green">E11</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E7:3_1_1_2_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="lang1.html#K4">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scm_comp.html#E5:3_1_1_2_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="bintree1.html#D4">BINTREE1:def 4</a></i>;<br/>
<b>thus </b><a NAME="E8:3_1_1_2_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">1,5</span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="txt" href="scm_comp.html#E3:3_1_1"><i><font color="Green">E6</font></i></a>, <a class="txt" href="scm_comp.html#E3:3_1_1_2_1"><i><font color="Green">E11</font></i></a>, <a class="txt" href="scm_comp.html#E5:3_1_1_2_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="scm_comp.html#E7:3_1_1_2_1"><i><font color="Green">E13</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:3_1_1_2"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">1,5</span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="scm_comp.html#E2:3_1_1"><i><font color="Green">E5</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E4:3_1_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="lang1.html#R1">==&gt;</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="lang1.html#K4">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="scm_comp.html#E3:3_1_1"><i><font color="Green">E6</font></i></a>, <a class="txt" href="scm_comp.html#E2:3_1_1_2"><i><font color="Green">E11</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:3_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K6">NonTerminals</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scm_comp.html#E6:3_1_1"><i><font color="Green">E9</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:3_1_1"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="dtconstr.html#V1">with_terminals</a>
 
<b>by </b><i><a class="txt" href="scm_comp.html#E5:3_1_1"><i><font color="Green">E8</font></i></a>, <a class="ref" href="dtconstr.html#D6">DTCONSTR:def 6</a></i>;<br/>
<a NAME="E9:3_1_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="dtconstr.html#V2">with_nonterminals</a>
 
<b>by </b><i><a class="txt" href="scm_comp.html#E7:3_1_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="dtconstr.html#D7">DTCONSTR:def 7</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:3_1_1_3"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K6">NonTerminals</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:3_1_1_3"/><i><font color="Green">E14</font></i>: 
(  <a href="ami_3.html#K15">dl.</a> 0 <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a>  &amp;  <a href="ami_3.html#K15">dl.</a> 1 <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a>  )
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="ami_3.html#K15">dl.</a> 0, <font color="Maroon">c<sub>4</sub></font> =  <a href="ami_3.html#K15">dl.</a> 1 as   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="scm_comp.html#E2:3_1_1"><i><font color="Green">E5</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E4:3_1_1_3"/>
(  <a href="trees_4.html#K2">root-tree</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="trees_4.html#K2">root-tree</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="scm_comp.html#E5:3_1_1"><i><font color="Green">E8</font></i></a>, <a class="txt" href="scm_comp.html#E2:3_1_1_3"><i><font color="Green">E14</font></i></a>, <a class="ref" href="dtconstr.html#D4">DTCONSTR:def 4</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="lang1.html#K4">*&gt;</a></span> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="finseq_2.html#T15">FINSEQ_2:15</a></i>;<br/><i><font color="Green">E15</font></i>:  <a href="trees_3.html#K16">roots</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> </span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="dtconstr.html#T6">DTCONSTR:6</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="trees_4.html#T3">TREES_4:3</a></i>
<br/>.= 
<span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span>
<b>by </b><i><a class="ref" href="trees_4.html#T3">TREES_4:3</a></i>
;<br/><b>take </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font>;<br/><b>thus </b><a NAME="E7:3_1_1_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="trees_3.html#K16">roots</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="scm_comp.html#E3:3_1_1"><i><font color="Green">E6</font></i></a>, <a class="txt" href="scm_comp.html#E7:3_1_1"><i><font color="Green">E10</font></i></a>, <a class="txt" href="scm_comp.html#E1:3_1_1_3"><i><font color="Green">E13</font></i></a>, <a class="txt" href="scm_comp.html#E6:3_1_1_3"><i><font color="Green">E15</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E11:3_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> is <a href="dtconstr.html#V3">with_useful_nonterminals</a>
 
<b>by </b><i><a class="ref" href="dtconstr.html#D8">DTCONSTR:def 8</a></i>;<br/>
<b>hence </b><a NAME="E12:3_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V3">empty</a> <a href="lang1.html#V1">strict</a> <a href="dtconstr.html#V1">with_terminals</a> <a href="dtconstr.html#V2">with_nonterminals</a> <a href="dtconstr.html#V3">with_useful_nonterminals</a> <a href="bintree1.html#V3">binary</a>  <a href="lang1.html#L1">DTConstrStr</a>  st <br/>(  <a href="dtconstr.html#K6">Terminals</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a>  &amp;  <a href="dtconstr.html#K7">NonTerminals</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">1,5</span><a href="zfmisc_1.html#K2">:]</a></span> &amp; ( for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Olive">b<sub>1</sub></font> holds <br/>( <font color="Olive">b<sub>2</sub></font> <a href="lang1.html#R1">==&gt;</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> iff <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">1,5</span><a href="zfmisc_1.html#K2">:]</a></span> ) ) )
 <b>by </b><i><a class="txt" href="scm_comp.html#E3:3_1_1"><i><font color="Green">E6</font></i></a>, <a class="txt" href="scm_comp.html#E5:3_1_1"><i><font color="Green">E8</font></i></a>, <a class="txt" href="scm_comp.html#E7:3_1_1"><i><font color="Green">E10</font></i></a>, <a class="txt" href="scm_comp.html#E8:3_1_1"><i><font color="Green">E11</font></i></a>, <a class="txt" href="scm_comp.html#E9:3_1_1"><i><font color="Green">E12</font></i></a></i>;<br/>


</div>
