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

<b>take </b><font color="Maroon" title="c1">G</font> =  <a href="lang1.html#K10" title="LANG1:func.10">EmptyGrammar</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>

<a NAME="E1:39_1_1"/><i><font color="Green" title="E19">A1</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; the <a href="lang1.html#U1" title="LANG1:sel.1">Rules</a> of <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<b>by </b><i><a class="ref" href="lang1.html#D7" target="_self" title="LANG1:def.7">Def7</a></i>;<br/>
<b>thus </b><a NAME="E2:39_1_1"/>
<font color="Maroon" title="c1">G</font> is <a href="lang1.html#V3" title="LANG1:attr.3">efective</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:39_1_1_1"/>
not  <a href="lang1.html#K7" title="LANG1:func.7">Lang</a> <font color="Maroon" title="c1">G</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="lang1.html#T11" target="_self" title="LANG1:th.11">Th11</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="lang1.html#D11" target="_self" title="LANG1:def.11">LANG1:def 11</a><br/>

<a NAME="E2:39_1_1_1"/>
( the <a href="lang1.html#U2" title="LANG1:sel.2">InitialSym</a> of <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<b>by </b><i><a class="txt" href="lang1.html#E1:39_1_1"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:39_1_1_1"/><b>then </b>
( the <a href="lang1.html#U2" title="LANG1:sel.2">InitialSym</a> of <font color="Maroon" title="c1">G</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a>  <a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> &amp;  <a href="lang1.html#K6" title="LANG1:func.6">NonTerminals</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">s</font> where <font color="Olive" title="b1">s</font> is   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c1">G</font> :  ex <font color="Olive" title="b2">n</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> st <font color="Olive" title="b1">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b2">n</font> </span>}</span>  )
 
<b>by </b><i><a class="txt" href="lang1.html#E1:39_1_1"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="lang1.html#D1" target="_self" title="LANG1:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E4:39_1_1_1"/>
the <a href="lang1.html#U2" title="LANG1:sel.2">InitialSym</a> of <font color="Maroon" title="c1">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lang1.html#K6" title="LANG1:func.6">NonTerminals</a> <font color="Maroon" title="c1">G</font>
 ;<br/>

<b>thus </b><a NAME="E5:39_1_1_1"/>
for <font color="Olive" title="b1">s</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lang1.html#K5" title="LANG1:func.5">Terminals</a> <font color="Maroon" title="c1">G</font> holds <br/> ex <font color="Olive" title="b2">p</font> being  <a href="lang1.html#NM2" title="LANG1:NM.2">String</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lang1.html#K7" title="LANG1:func.7">Lang</a> <font color="Maroon" title="c1">G</font> &amp; <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Olive" title="b2">p</font> )
 <b>by </b><i><a class="ref" href="lang1.html#T10" target="_self" title="LANG1:th.10">Th10</a></i>;<br/>


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

<b>thus </b><a NAME="E3:39_1_1"/>
the <a href="lang1.html#U1" title="LANG1:sel.1">Rules</a> of <font color="Maroon" title="c1">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="txt" href="lang1.html#E1:39_1_1"><i><font color="Green" title="E19">A1</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="lang1.html#D12" target="_self" title="LANG1:def.12">LANG1:def 12</a><br/>


</div>
