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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:32"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E2:32"/><i><font color="Green">E17</font></i>: 
 <a href="lang1.html#K5" target="_self">Terminals</a> <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="lang1.html#E1:32"><i><font color="Green">E16</font></i></a>, <a class="ref" href="lang1.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E3:32"/><i><font color="Green">E18</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> &amp; the <a href="lang1.html#U2" target="_self">InitialSym</a> of <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="lang1.html#U1" target="_self">Rules</a> of <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="lang1.html#D8" target="_self">Def8</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="lang1.html#NM1">Symbol</a> of <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>thus </b><a NAME="E5:32"/>
 <a href="lang1.html#K7" target="_self">Lang</a> <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="tarski.html#K1">}</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="32_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>6</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="E1:32_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K7" target="_self">Lang</a> <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="lang1.html#NM2">String</a> of <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:32_1"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a>  <a href="lang1.html#K5" target="_self">Terminals</a> <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="lang1.html#R3" target="_self">is_derivable_from</a> <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default">the <a href="lang1.html#U2" target="_self">InitialSym</a> of <span class="p2">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> )
 ;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E5:32_1"/><i><font color="Green">E20</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default">the <a href="lang1.html#U2" target="_self">InitialSym</a> of <span class="p2">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="lang1.html#NM2">String</a> of <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="lang1.html#R2" target="_self">==&gt;</a> <font color="Olive">b<sub>3</sub></font> ) ) )
 <b>by </b><i><a class="txt" href="lang1.html#E3:32_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="lang1.html#D5" target="_self">Def5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:32_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span>
 ;<br/><a NAME="E2:32_1_1"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T55">FINSEQ_1:55</a></i>;<br/><a NAME="E3:32_1_1"/><b>then </b>
<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>7</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:32_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="lang1.html#E1:32"><i><font color="Green">E16</font></i></a>, <a class="txt" href="lang1.html#E2:32"><i><font color="Green">E17</font></i></a>, <a class="txt" href="lang1.html#E3:32_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<a NAME="E7:32_1"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="lang1.html#E3:32"><i><font color="Green">E18</font></i></a>, <a class="txt" href="lang1.html#E5:32_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</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="lang1.html#NM2">String</a> of <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span><b> such that </b><br/><a NAME="E9:32_1"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="lang1.html#R2" target="_self">==&gt;</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="lang1.html#E5:32_1"><i><font color="Green">E20</font></i></a></i>;<br/>
<a NAME="E10:32_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="lang1.html#R1" target="_self">==&gt;</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="lang1.html#E3:32"><i><font color="Green">E18</font></i></a>, <a class="txt" href="lang1.html#E5:32_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="lang1.html#E9:32_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="lang1.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E11:32_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="lang1.html#E3:32"><i><font color="Green">E18</font></i></a>, <a class="ref" href="lang1.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E12:32_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E13:32_1"/><b>then </b><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> 2 )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:32_1_2"/>
2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> being   <a href="lang1.html#NM2">String</a> of <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:32_1_2"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#R2" target="_self">==&gt;</a> <font color="Maroon">c<sub>12</sub></font> )
 <b>by </b><i><a class="txt" href="lang1.html#E5:32_1"><i><font color="Green">E20</font></i></a></i>;<br/><a NAME="E4:32_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="lang1.html#R1" target="_self">==&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="lang1.html#E9:32_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="lang1.html#E13:32_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="lang1.html#E3:32_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="lang1.html#T4" target="_self">Th4</a></i>;<br/><a NAME="E5:32_1_2"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>12</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="lang1.html#E3:32"><i><font color="Green">E18</font></i></a>, <a class="ref" href="lang1.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E6:32_1_2"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>12</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:32_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="lang1.html#E1:32"><i><font color="Green">E16</font></i></a>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/></div><b>end;</b></div>
<a NAME="E15:32_1"/><b>then </b>
( 2 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i><a class="txt" href="lang1.html#E7:32_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E16:32_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="lang1.html#E3:32_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="lang1.html#E5:32_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="lang1.html#E9:32_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="lang1.html#E13:32_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<b>hence </b><a NAME="E17:32_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


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

<b>let </b><font color="Maroon">c<sub>6</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="E6:32"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E7:32"/><b>then </b><i><font color="Green">E19</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="lang1.html#U1" target="_self">Rules</a> of <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="txt" href="lang1.html#E3:32"><i><font color="Green">E18</font></i></a>, <a class="ref" href="finseq_1.html#T55">FINSEQ_1:55</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E8:32"/><b>then </b>
the <a href="lang1.html#U2" target="_self">InitialSym</a> of <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lang1.html#R1" target="_self">==&gt;</a> <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="lang1.html#E3:32"><i><font color="Green">E18</font></i></a>, <a class="ref" href="lang1.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E9:32"/><b>then </b>
<span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default">the <a href="lang1.html#U2" target="_self">InitialSym</a> of <span class="p2">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> <a href="lang1.html#R2" target="_self">==&gt;</a> <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="lang1.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E10:32"/><b>then </b>
<span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="lang1.html#K3" target="_self">*&gt;</a></span> <a href="lang1.html#R3" target="_self">is_derivable_from</a> <span class="p1"><a href="lang1.html#K3" target="_self">&lt;*</a><span class="default">the <a href="lang1.html#U2" target="_self">InitialSym</a> of <span class="p2">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="lang1.html#K3" target="_self">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="lang1.html#T7" target="_self">Th7</a></i>;<br/>
<b>hence </b><a NAME="E11:32"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K7" target="_self">Lang</a> <span class="p1">(<span class="default"><a href="lang1.html#K11" target="_self">SingleGrammar</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="lang1.html#E2:32"><i><font color="Green">E17</font></i></a>, <a class="txt" href="lang1.html#E7:32"><i><font color="Green">E19</font></i></a></i>;<br/>


</div>
